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study help
mathematics
a first course in differential equations

Questions and Answers of A First Course in Differential Equations

Solve the given boundary-value problem.y'' + 3y = 6x, y(0) = 0, y'(0) = y(1) = 0
Solve the given boundary-value problem.y'' + 3y = 6x, y(0) = 0, y(1) + y'(1) = 0
Solve the given boundary-value problem.y'' – 2y' + 2y = 2x – 2, y(0) = 0, y(π) = π
Solve the given boundary-value problem.y'' + y = x2 + 1, y(0) = 5, y(1) = 0
Solve the given initial-value problem.y''' + 8y = 2x - 5 + 8e-2x, y(0) = -5, y'(0) = 3, y''(0) = -4
Solve the given initial-value problem. y" – 2y" + y' = 2 – 24e* + 40e, y(0) = 2 %3D 2.
Solve the given initial-value problem. d'x + wx = Focos t, x(0) = 0, x'(0) = 0 %3D %3D di?
Solve the given initial-value problem. d'x + wx = Fo sin wt, x(0) = 0, x'(0) = 0 %3D %3D %3D dr?
Solve the given initial-value problem.y'' - y = cosh x, y(0) = 2, y'(0) = 12
Solve the given initial-value problem.y'' + 4y' + 5y = 35e-4x, y(0) = -3, y'(0) = 1
Solve the given initial-value problem.y'' + 4y' + 4y = (3 + x)e-2x, y(0) = 2, y'(0) = 5
Solve the given initial-value problem.5y'' + y' = -6x, y(0) = 0, y' (0) = -10
Solve the given initial-value problem.2y'' + 3y' – 2y = 14x2 – 4x – 11, y(0) = 0 y'(0) = 0
Solve the given initial-value problem.y'' + 4y = -2, y(π/8) = ½ y'(π/8) = 2
Solve the given differential equation by undetermined coefficients.y(4) - y'' = 4x + 2xe-x
Solve the given differential equation by undetermined coefficients.y(4) + 2y'' + y = (x - 1)2
Solve the given differential equation by undetermined coefficients.y''' – y'' - 4y' + 4y = 5 - ex + e2x
Solve the given differential equation by undetermined coefficients.y''' - 3y'' + 3y' - y = x - 4ex
Solve the given differential equation by undetermined coefficients.y''' - 2y'' = 4y' + 8y = 6xe2x
Solve the given differential equation by undetermined coefficients.y''' - 6y = 3 - cos x
Solve the given differential equation by undetermined coefficients.y'' - 2y'' - 24y = 16 - (x + 2)e4x
Solve the given differential equation by undetermined coefficients.y'' + 2y' + y = sin x - 3 cos 2x
Solve the given differential equation by undetermined coefficients.y'' - 2y' + 2y = e2x(cos x - 3 sin x)
Solve the given differential equation by undetermined coefficients.y'' - 2y' + 5y = ex cos 2x
Solve the given differential equation by undetermined coefficients.y' - 5y' = 2x3 - 4x2 - x + 6
Solve the given differential equation by undetermined coefficients.y'' + y = 2x sinx
Solve the given differential equation by undetermined coefficients.y'' – 4y = (x2 - 3)sin 2x
Solve the given differential equation by undetermined coefficients.y'' + 4y = 3 sin2x
Solve the given differential equation by undetermined coefficients.y'' – 16y = 2e4x
Solve the given differential equation by undetermined coefficients.y'' – y' + 1/4y = 3 + ex/2
Solve the given differential equation by undetermined coefficients.y'' + 2y' = 2x + 5 – e-2x
Solve the given differential equation by undetermined coefficients.y'' + y' = -3
Solve the given differential equation by undetermined coefficients.4y'' – 4y' – 3y = cos 2x
Solve the given differential equation by undetermined coefficients.y'' + 3y = -48x2e3x
Solve the given differential equation by undetermined coefficients.y'' – 8y' + 20y = 100x2 – 26xe2
Solve the given differential equation by undetermined coefficients.1/4y'' + y' + y = x2 – 2x
Solve the given differential equation by undetermined coefficients.y'' + y' -6y = 2x
Solve the given differential equation by undetermined coefficients.y'' – 10y' + 25y = 30x + 3
Solve the given differential equation by undetermined coefficients.4y'' + 9y = 15
Solve the given differential equation by undetermined coefficients.y'' + 3y' + 2y = 6
Use a CAS as an aid in solving the auxiliary equation. Form the general solution of the differential equation. Then use a CAS as an aid in solving the system of equations for the coefficients ci, i =
Use a CAS as an aid in solving the auxiliary equation. Form the general solution of the differential equation. Then use a CAS as an aid in solving the system of equations for the coefficients ci, i =
Use a computer either as an aid in solving the auxiliary equation or as a means of directly obtaining the general solution of the given differential equation. If you use a CAS to obtain the general
Use a computer either as an aid in solving the auxiliary equation or as a means of directly obtaining the general solution of the given differential equation. If you use a CAS to obtain the general
Use a computer either as an aid in solving the auxiliary equation or as a means of directly obtaining the general solution of the given differential equation. If you use a CAS to obtain the general
Use a computer either as an aid in solving the auxiliary equation or as a means of directly obtaining the general solution of the given differential equation. If you use a CAS to obtain the general
Consider the boundary-value problem y'' + λy = 0, y(0) = 0, y(π/2) = 0. Discuss: Is it possible to determine values of λ so that the problem possesses(a) Trivial solutions?(b) Nontrivial solutions?
Solve the given boundary-value problem.y'' + 2y' +2y = 0, y(0) = 1, y(π) = 1
Solve the given boundary-value problem.y'' + y = 0, y'(0) = 0, y'(π/2) = 0
Solve the given differential equation by separation of variables.
Solve the given differential equation by separation of variables. dy =xVT- y dx
Solve the given differential equation by separation of variables. dy _ху + 2y dx ху — Зу +x — 3 - х — 2
Solve the given differential equation by separation of variables. dy ху + 3x - у -3 - 3 dx ху — 2х + 4у —8
Solve the given differential equation by separation of variables.dN/dt + N = Ntet+2
Solve the given differential equation by separation of variables.dP/dt = P - P2
Solve the given differential equation by separation of variables.dQ/dt = k(Q - 70)
Suppose that dA/dt = 0.0004332 A(t) represents a mathematical model for the radioactive decay of radium- 226, where A(t) is the amount of radium (measured in grams) remaining at time t (measured in
The number of field mice in a certain pasture is given by the function 200 10t, where time t is measured in years. Determine a differential equation governing a population of owls that feed on the
In Problems 1 and 2, y = 1/(1 + c1e-x) is a one-parameter family of solutions of the first-order DE y' = y - y2. Find a solution of the first-order IVP consisting of this differential equation and
In Problems 1 and 2, y = 1/(1 + c1e-x) is a one-parameter family of solutions of the first-order DE y' = y - y2. Find a solution of the first-order IVP consisting of this differential equation and

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