Finding Complementary Fcn of ODE: (3 + t) x"(t) + (2 + t) x'(t) - x(t) = (3 + t)^2

[AFraggers]

Finding Complementary Fcn of ODE: (3 + t) x"(t) + (2 + t) x'(t) - x(t) = (3 + t)^2

I've been given a question: Consider the initial value problem

(3 + t) x"(t) + (2 + t) x'(t) - x(t) = (3 + t)^2

subject to x(0) = 0 and x'(0) = 1.

Determine the complementary function for the homogeneous equation which satisfies the given initial conditions.

I know how to find the complementary function on any other problems but this one I cant quite grasp. Can you expand the LHS and remove the t values and then make it equal to 0 or am i wrong?

Any help will be appreciated.

 

[HallsofIvy]

What kinds of differential equations are you used to? This is not a "constant coefficients" equation, which you seem to be thinking of, nor is it quite an "equi-potential" equation. Where did you get it?