Find the general solution of the given differential equations, the largest interval over which the solution is defied and determine whether there are any transient terms in the solution.

I mainly need someone to check my answer and if they're wrong to help me correct the mistakes I made

$\displaystyle dy/dx - 2y = x^2 + 5$

I found the integrating factor to be $\displaystyle e^-^2^x$

Multiplied both sides by integrating factor and integrated to get:

$\displaystyle e^-^2^xy = -1/2x^2e^-^2^x - 1/2xe^-^2^x - 5/2e^-^2^x + C$

$\displaystyle y = -x^2/2 - x/2 - 5/2 + Ce^2^x$

Largest interval I think would be (-∞, ∞) and I don't think there are any transient terms

Thanks in advance.