Non-homogeneous Linear Equations


Part c: Sine and Cosine Functions


Each differential equation has a sine and/or cosine function on the right hand side.

Find a particular solution for each equation.

No initial conditions are given because you are only asked to find one solution.


Please enter any multiplication explicitly with * symbols so the parcer can understand your answer, like this:

2t3e5t2⟶2∗t3∗e(5∗t2).2t^3e^{5t^2} \longrightarrow 2*t^3*e^{(5*t^2)}.

Problem 1

Find a family of functions that solves the equation and satisfies the conditions below.

y′′+2y=cos(t)y'' + 2y = cos(t)

Initial Conditions to Check: