Solving for Particular Solution in a Differential Equation

[rbailey5]

Homework Statement

determine the particular solution for the differential equation 2x^double prime+x=3t^2

Homework Equations

The Attempt at a Solution

since F(t)=3t^2 I used At^2+Bt+C and the first derivative is 2A+B

plugging back in I get
At^2+(4A+B)t+(2B+C)=3t^2

is this correct?
how do I solve for the variables?

 

[rbailey5]

I got A=3, B=-12, and C=24 does that look right?