The equation y''+y'-3=x^2 if y=Ax^2+Bx+c satisfies the give equation find A,B and C?

y' = 2Ax + B
y'' = 2A

2Ax + B + 2A - 3 = x^2 I hope you notice that this stuff is a lot easier to read with some spaces in it.

You have three unknowns and only one equation. No solution.