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.

Printable View

- Feb 23rd 2009, 03:16 PMmillerstDifferenation/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 PMskeeter
$\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.