1.

1. Solve the following differential equation by separation of variables. dy -7x2 tan(y) dx O y = sin 1(e7 /3) + C O y= eC+723/3 O y = sin 1(eC+723/3 O y=ex /3 + C2. Show that y = 5est + 2 sin a is a solution of the initial value problem y - 3y = 2 cos x - 6 sin x, with y (0) = 5.3. Solve the following differential equation with the given initial value. dy = 26, y(1) = 0 dx O 6 y = + C O 6 y = J ac + O y = JO O 6 y =D J 4.a21 -year-old student is offered an opportunity to invest some money in a retirement account that pays 8% annual interest compounded continuously. How much does the student need to invest today to have $1 million when he retires at age 65? What if he could earn 9% annual interest compounded continuously instead? (O $27323.72,$17422.37 (O $20979.92,$20771.16 (O $40617119.24, $40212972.15 () $29599.44,$19063.11 \f1. Sketch the slope field for 2 CC x sin y2. For the differential equation dy dx 3x - y with the initial condition y(0) = 6 and Ax = 0.4, use Euler's Method to estimate the y-value at x = 2. 3.700 O 2.966 O 2.640 O 2.544d [J 3.By hand, sketch the slope field for dy * 2ywherez = [-3,3] andy = [-3, 3]. T Then sketch a graph of the solution that satisfies y(0) = 1 W Q 4. For the differential equation dy = e("+y) with the initial condition y(0) = -5 and Ax = 0.6, use dx Euler's Method to estimate the y-value at x = 3. -4.950 O -4.975 O -4.989 -4.903W 5. For the differential equation dy dx = -3y with the initial condition y(0) = 5 and Ax = 0.6, use Euler's Method to estimate the y-value at x = 3. O -1.638 O -2.560 O 2.048 O 1.3116. By hand, sketch the slope field for dy = xe* where x = [-3, 3] and y = [-3, 3]. dx Then sketch a graph of the solution that satisfies y(-1) = 0