Thread: solving for particular soln in nonhomogenous differential equation

1. solving for particular soln in nonhomogenous differential equation

i'm solving the differential equation x''+x'-t=0 with the conditions x(0)=0 and x'(0)=0. i got that x_h=0 but i forget how to find x_p. can someone refresh me on how to find x_p in this case?

2. Originally Posted by squarerootof2
i'm solving the differential equation x''+x'-t=0 with the conditions x(0)=0 and x'(0)=0. i got that x_h=0 but i forget how to find x_p. can someone refresh me on how to find x_p in this case?
Your equation is $x'' + x = t$.
Note the RHS is a polynomial, thus, look for a solution of the form $x_p=at+b$.

EDIT: Suppose the equation was $x''+x' = t$.
Then look for a polynomial $x_p = at^2+bt+c$.

3. Originally Posted by ThePerfectHacker
Your equation is $x'' + x{\color{red}'} = t$.
Note the RHS is a polynomial, thus, look for a solution of the form $x_p=at+b$.
The smallest of erratums (in red).

Even obvious typos can cause anxiety and doubt amongst the ..... anxious.

(I can hear TPH saying "Dash it!")