# Differenation/Differential Equation

• Feb 23rd 2009, 03:16 PM
millerst
Differenation/Differential Equation
Hi, I'm lost with this question. Never done differential equations before, yet... (Wondering)

From the equation y'' + y' - 2y = x^2, find constants A,B and C such that the function y = Ax2 + Bx + C satisfies the equation.
• Feb 23rd 2009, 03:23 PM
skeeter
Quote:

Originally Posted by millerst
Hi, I'm lost with this question. Never done differential equations before, yet... (Wondering)

From the equation y'' + y' - 2y = x^2, find constants A,B and C such that the function y = Ax2 + Bx + C satisfies the equation.

\$\displaystyle y = Ax^2 + Bx + C
\$

\$\displaystyle y' = 2Ax + B\$

\$\displaystyle y'' = 2A\$

\$\displaystyle y'' + y' - 2y = x^2\$

\$\displaystyle 2A + (2Ax + B) - 2(Ax^2 + Bx + C) = x^2\$

\$\displaystyle -2Ax^2 + (2A-2B)x + (2A + B - 2C) = x^2\$

match up the coefficients ...

\$\displaystyle -2A = 1\$

\$\displaystyle 2A - 2B = 0\$

\$\displaystyle 2A + B - 2C = 0\$

solve for A, B, and C.