Differential Equations Answers

solve the D.E dy/dx = (6x^5-2x+1)/(cosy+e^y)

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.