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Solving Differential Equation

Hi,

Could some one give me a pointer with this one please?

dy/dx + y = e^-x

I know that the complementary function will be Ae^-x, but I'm a bit stuck with the particular integral.
Original post by chris238973
Hi,

Could some one give me a pointer with this one please?

dy/dx + y = e^-x

I know that the complementary function will be Ae^-x, but I'm a bit stuck with the particular integral.


Clearly, the RHS of the ODE appears in the complimentary function.

Therefore you cannot use yp=λe−xy_p = \lambda e^{-x}... but you can use yp=λxe−xy_p = \lambda x e^{-x}.
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chris238973
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Original post by RDKGames
Clearly, the RHS of the ODE appears in the complimentary function.

Therefore you cannot use yp=λe−xy_p = \lambda e^{-x}... but you can use yp=λxe−xy_p = \lambda x e^{-x}.


thanks.

I've got:

ycf = Ae^-x

yp = (Cx + D)e^-x

therefore: dy/dx = Ce^-x - (Cx + D)e^-x

subbing back into original equation gave me:

C = 1 and D = 0

therefore: yp = xe^-x

So, the general solution:

ygs = Ae^-x + xe^-x

but seeing your suggestion of, yp = Bxe^-x, i could of skipped a few steps.

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