Non-homogeneous Linear Equations


Part a: Exponential Functions


Each differential equation has an exponential 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:

2t3e5t22t3e(5t2).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+y=32ety'' + 2y' + y = 32e^t

Initial Conditions to Check: