- Use method of undetermined coefficients...

Question

asylum15 · Answer

To solve this:

asylum15 · Answer

Here is the solution ->

phi · Answer

First find the solution to the homogenous equation (= zero rather than what is on the right hand side)

anonymous · Answer

For the nonhomogeneous solution guess, try $y_p=Ax^2+Bx+C$:
$$y_p'=2Ax+B\
y_p''=2A$$
Substitute into the equation:
$$y''+3y'+5y=10x^2-1\
2A+6Ax+3B+5Ax^2+5Bx+5C=10x^2-1\
5Ax^2+(6A+5B)x+(2A+3B+5C)=10x^2-1$$
Match up coefficients, solve for $A,B,C$:
$$\begin{cases}5A=10\6A+5B=0\2A+3B+5C=-1\end{cases}$$
Whatever you get for the nonhomogeneous solution will not match up to the solution you're given, however. Check to make sure you posted the right equation/solution.