Differential Equations Answers

dx/2xz=dy/2yz=dz/z^2-x^2-y^2

Use the linearity property of Laplace transform to find L[5e^-2t + t + 2e^2t]

 Find the Laplace transform, if it exists, of each of the following functions

(a) f(t) = e^at

(b) f(t) = 1

(c) f(t) = t 

Find the general solution to y'' − y' − 2y = 2e^3x

Find the general solution to y'' + 4y' + 3y = x.

Given that p(x) = −2 is a particular solution to y'' − 3y' − 4y = 8, write the general solution and verify that the general solution satisfies the equation. 

Given that p(x) = x is a particular solution to the differential equation y'' + y = x write the generalized solution and check by verifying that the solution satisfies the equation.