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study help
mathematics
precalculus
Questions and Answers of
Precalculus
Solve the differential equation.d2y/dx2 + dy/dx - 2y = x2
Solve the differential equation.d2y/dx2 - 4 dy/dx + 5y = e-x
Solve the differential equation.y'' + 8y' + 16y = 0
Solve the differential equation.y'' + 3y = 0
Solve the differential equation.y'' - 2y' + 10y = 0
Solve the differential equation.4y'' - y = 0
Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement.The equation y'' - y = ex has a particular
Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement.The general solution of y'' - y = 0 can be
Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement.If y1 and y2 are solutions of y0 + 6y' + 5y =
The solution of the initial-value problem x2y'' + xy' + x2y = 0 y(0) = 1 y'(0) = 0 is called a Bessel function of order 0.(a) Solve the initial-value problem to find a power series expansion for the
Use power series to solve the differential equation.y'' + x2y9 + xy = 0, y(0) = 0, y'(0) = 1
Use power series to solve the differential equation.y'' + x2y = 0, y(0) = 1, y'(0) = 0
Use power series to solve the differential equation.y'' - xy' - y = 0, y(0) = 1, y'(0) = 0
Use power series to solve the differential equation.y'' = xy
Use power series to solve the differential equation.(x - 1) y'' + y' = 0
Use power series to solve the differential equation.y'' = y
Use power series to solve the differential equation.y'' + xy' + y = 0
Use power series to solve the differential equation.(x - 3)y' + 2y = 0
Use power series to solve the differential equation.y' = x2y
Use power series to solve the differential equation.y' = xy
Use power series to solve the differential equation.y' - y = 0
Verify that the solution to Equation 1 can be written in the form x(t) = A cos(wt + ).
The battery in Exercise 14 is replaced by a generator producing a voltage of E(t) = 12 sin 10t.(a) Find the charge at time t.(b) Graph the charge function.
The battery in Exercise 13 is replaced by a generator producing a voltage of E(t) = 12 sin 10t. Find the charge at time t.
A series circuit contains a resistor with R = 24 V, an inductor with L = 2 H, a capacitor with C = 0.005 F, and a 12-V battery.The initial charge is Q = 0.001 C and the initial current is 0.(a) Find
A series circuit consists of a resistor with R = 20 Ω, an inductor with L = 1 H, a capacitor with C = 0.002 F, and a 12-V battery. If the initial charge and current are both 0, find the charge and
Consider a spring subject to a frictional or damping force.(a) In the critically damped case, the motion is given by x = c1ert + c2tert. Show that the graph of x crosses the t-axis whenever c1 and c2
Show that if w0 ≠ w, but w/w0 is a rational number, then the motion described by Equation 6 is periodic.
Suppose a spring has mass m and spring constant k and let w = √k/m. Suppose that the damping constant is so small that the damping force is negligible. If an external force F(t) = F0 cos w0t is
A spring has a mass of 1 kg and its damping constant is c = 10. The spring starts from its equilibrium position with a velocity of 1 m/s. Graph the position function for the following values of the
A spring has a mass of 1 kg and its spring constant is k = 100. The spring is released at a point 0.1 m above its equilibrium position. Graph the position function for the following values of the
For the spring in Exercise 4, find the damping constant that would produce critical damping.
For the spring in Exercise 3, find the mass that would produce critical damping.
A force of 13 N is needed to keep a spring with a 2-kg mass stretched 0.25 m beyond its natural length. The damping constant of the spring is c = 8.(a) If the mass starts at the equilibrium position
A spring with a mass of 2 kg has damping constant 14, and a force of 6 N is required to keep the spring stretched 0.5 m beyond its natural length. The spring is stretched 1 m beyond its natural
A spring with an 8-kg mass is kept stretched 0.4 m beyond its natural length by a force of 32 N. The spring starts at its equilibrium position and is given an initial velocity of 1 m/s. Find the
A spring has natural length 0.75 m and a 5-kg mass. A force of 25 N is needed to keep the spring stretched to a length of 1 m. If the spring is stretched to a length of 1.1 m and then released with
Solve the differential equation using the method of variation of parameters.y'' + 4y' + 4y = e-2x/x3
Solve the differential equation using the method of variation of parameters.y'' - 2y' + y = eX/1 + x2
Solve the differential equation using the method of variation of parameters.y'' + 3y' + 2y = sin(ex)
Solve the differential equation using the method of variation of parameters.y'' - 3y' + 2y = 1/1 + e-x
Solve the differential equation using the method of variation of parameters.y'' + y = sec3x, 0 < x < π/2
Solve the differential equation using the method of variation of parameters.y'' + y = sec2x, 0 < x < π/2
Solve the differential equation using (a) undetermined coefficients and (b) variation of parameters.y'' - y' = ex
Solve the differential equation using (a) undetermined coefficients and (b) variation of parameters.y'' - 2y' + y = e-x
Solve the differential equation using (a) undetermined coefficients and (b) variation of parameters.y'' - 2y' - 3y = x + 2
Solve the differential equation using (a) undetermined coefficients and (b) variation of parameters.4y'' + y = cos x
Write a trial solution for the method of undetermined coefficients. Do not determine the coefficients.y'' + 4y = e3x + x sin 2x
Write a trial solution for the method of undetermined coefficients. Do not determine the coefficients.y'' + 2y' + 10y = x2e-x cos 3x
Write a trial solution for the method of undetermined coefficients. Do not determine the coefficients.y'' + 3y' - 4y = (x3 + x)ex
Write a trial solution for the method of undetermined coefficients. Do not determine the coefficients.y'' - 3y' + 2y = ex + sin x
Write a trial solution for the method of undetermined coefficients. Do not determine the coefficients.y'' + 4y = cos 4x + cos 2x
Write a trial solution for the method of undetermined coefficients. Do not determine the coefficients.y'' - y' - 2y = xex cos x
Graph the particular solution and several other solutions. What characteristics do these solutions have in common?y'' + 4y = e-x
Graph the particular solution and several other solutions. What characteristics do these solutions have in common?y'' + 3y' + 2y = cos x
Solve the differential equation or initial-value problem using the method of undetermined coefficients.y'' + y' - 2y = x + sin 2x, y(0) = 1, y'(0) = 0
Solve the differential equation or initial-value problem using the method of undetermined coefficients.y'' - y' = xex, y(0) = 2, y'(0) = 1
Solve the differential equation or initial-value problem using the method of undetermined coefficients.y'' - y = xe-x, y(0) = 0, y'(0) = 1
Solve the differential equation or initial-value problem using the method of undetermined coefficients.y'' - 2y' + 5y = sin x, y(0) = 1, y(0) = 1
Solve the differential equation or initial-value problem using the method of undetermined coefficients.y'' - 4y' + 4y = x - sin x
Solve the differential equation or initial-value problem using the method of undetermined coefficients.y'' - 4y' + 5y = e-x
Solve the differential equation or initial-value problem using the method of undetermined coefficients.y'' - 2y' + 2y = x + ex
Solve the differential equation or initial-value problem using the method of undetermined coefficients.9y'' + y = e-x
Solve the differential equation or initial-value problem using the method of undetermined coefficients.y'' - 3y' = sin 2x
Solve the differential equation or initial-value problem using the method of undetermined coefficients.y'' + 2y' - 8y = 1 - 2x2
Consider the boundary-value problem y'' - 2y' + 2y = 0, y(a) = c, y(b) = d.(a) If this problem has a unique solution, how are a and b related?(b) If this problem has no solution, how are a, b, c, and
If a, b, and c are all positive constants and y(x) is a solution of the differential equation ay'' + by' + cy = 0, show that limx→∞ y(x) = 0.
Let L be a nonzero real number.(a) Show that the boundary-value problem y'' + λy = 0, y(0) = 0, y(L) = 0 has only the trivial solution y = 0 for the cases λ = 0 and λ < 0.(b) For the case λ
Solve the boundary-value problem, if possible.y'' + 4y' + 20y = 0, y(0) = 1, y(π) = e-2π
Solve the boundary-value problem, if possible.y'' + 4y' + 20y = 0, y(0) = 1, y(π) = 2
Solve the boundary-value problem, if possible.4y'' - 4y' + y = 0, y(0) = 4, y(2) = 0
Solve the boundary-value problem, if possible.y'' = y', y(0) = 1, y(1) = 2
Solve the boundary-value problem, if possible.y'' - 8y' + 17y = 0, y(0) = 3, y(π) = 2
Solve the boundary-value problem, if possible.y'' + 4y' + 4y = 0, y(0) = 2, y(1) = 0
Solve the boundary-value problem, if possible.y'' + 6y' = 0, y(0) = 1, y(1) = 0
Solve the boundary-value problem, if possible.y'' + 16y = 0, y(0) = -3, y(π/8) = 2
Solve the initial-value problem.4y'' + 4y' + 3y = 0, y(0) = 0, y'(0) = 1
Solve the initial-value problem.y'' - y' - 12y = 0, y(1) = 0, y'(1) = 1
Solve the initial-value problem.4y'' - 20y' + 25y = 0, y(0) = 2, y'(0) = -3
Solve the initial-value problem.y'' - 6y' + 10y = 0, y(0) = 2, y'(0) = 3
Solve the initial-value problem.3y'' - 2y' - y = 0, y(0) = 0, y'(0) = -4
Solve the initial-value problem.9y'' + 12y' + 4y = 0, y(0) = 1, y'(0) = 0
Solve the initial-value problem.y'' - 2y' - 3y = 0, y(0) = 2, y'(0) = 2
Solve the initial-value problem.y'' + 3y = 0, y(0) = 1, y'(0) = 3
Graph the two basic solutions along with several other solutions of the differential equation. What features do the solutions have in common?2d2y/dx2 + dy/dx - y = 0
Graph the two basic solutions along with several other solutions of the differential equation. What features do the solutions have in common?d2y/dx2 + 2dy/dx + 2y = 0
Graph the two basic solutions along with several other solutions of the differential equation. What features do the solutions have in common?4d2y/dx2 - 4dy/dx + y = 0
Solve the differential equation.3d2V/dt2 + 4dV/dt + 3V = 0
Solve the differential equation.d2R/dt2 + 6 dR/dt + 34R = 0
Solve the differential equation.2/d2y/dt2 + 2dy/dt - y = 0
Solve the differential equation.3y'' + 4y' - 3y = 0
Solve the differential equation.y'' - 4y' + 13y = 0
Solve the differential equation.y = y''
Solve the differential equation.3y'' = 4y'
Solve the differential equation.9y'' + 4y = 0
Solve the differential equation.y'' + 4y' + y = 0
Solve the differential equation.y'' + y' - 12y = 0
Solve the differential equation.y'' + 2y = 0
Solve the differential equation.y'' - 6y' + 9y = 0
Solve the differential equation.y'' - y' - 6y = 0
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