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10 cards from this deck
ad2ydx2+bdydx+cy=F(x)a\frac{d^2y}{dx^2} + b\frac{dy}{dx} + cy = F(x)adx2d2y+bdxdy+cy=F(x)
Solution to homogeneous equation (F(x)=0F(x) = 0F(x)=0)
Specific solution to non-homogeneous equation
Solve characteristic eqn assuming y=emxy = e^{mx}y=emx
C.F. + P.I.
ax2+bx+cax^2 + bx + cax2+bx+c
aekxae^{kx}aekx
asinλx+bcosλxa\sin\lambda x + b\cos\lambda xasinλx+bcosλx
Multiply by xxx
λxe2x\lambda x e^{2x}λxe2x
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