Question

The equation y'' + y' -2y = x^2 is called a differential equation because it involves an unknown function y and its derivatives y' and y''. Find constants A,B, and C such that the function y=Ax^2+Bx+c satisfies the equation

Answer 1

If y=Ax^2 + Bx + C
y' = 2Ax + B
y''= 1
Is what I have so far

Answer 2

BTW, this is a calculus I class

Answer 3

substitute those expressions for y, y', and y'' into the equation above

Answer 4

tell me what you get, or if you need more explanation

Answer 5

Y=AX^2+BX+C
Y'=2AX+B
Y''=2A
Y''+Y'-2Y=2A+2AX+B-2AX^2-2BX-2C=X^2, then
-2AX^2+(2A-2B)X+B-2C=X^2,and
-2A=1, and A=-1/2
2A-2B=0, then B=A=-1/2
B-2C=0, then C=B/2=-1/4