Differential Equations Answers

Solve

x^2y′′+ xy′− y =1/x + 1

Solve

x ^2y'′ + 2xy'− 12y = x^3log x.

8. Solve x

x^2y′′− 2xy′+ 2y = x^4sin(4 log x)

The equation of motion of a body is given by d²y/dt² + 4dy/dt + 13y = e^2tcost , where y is the distance and t is the time.

Determine a general solution for y in terms of t.

Determine the unique solution of the following differential equations by using Laplace transforms:

a. y"(t) - 6y'(t) + 9y(t) = t²e^3t if y'(0) = 6 and y(0) = 2

b. y"(t) - 2y'(t) + 3y(t) = e^-3t if y'(0) = 0 and y(0) = 0

Use two different methods to determine L^-1 {(11 - 3s)/ (s² + 2s -3)} Show that your answers are equal.

Find a general solution of the following differential equation

dy/dx - 5y = (xe^-2x)*y^-2

Solve the given initial value problem.

dy/dx = y(2x^2 +y^2)/2x^3

subject to y(1) = 1.

(d^3-5d^2+7d-3)y=0

(D^2+4D+3)y=2cos^2x