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# FP2: 2nd order differential equations - Substitution watch

1. I've found the complementary integral and got y=e^-x(Acosx + Bsinx) but I wasn't sure what to use to find my particular integral! Would it be y=lamdaE^mx or y=lamdaE^-x
2. (Original post by creativebuzz)

I've found the complementary integral and got y=e^-x(Acosx + Bsinx) but I wasn't sure what to use to find my particular integral! Would it be y=lamdaE^mx or y=lamdaE^-x
You can't use because it's part of the C.I, so what would you use instead?
3. (Original post by Jordan\)
You can't use because it's part of the C.I, so what would you use instead?
λe^-x is not part of the C.F?
4. (Original post by Gome44)
λe^-x is not part of the C.I?
Oh I read it wrong, I just saw it in the C.F It would be fine to just use λe^-x then wouldn't it?
5. (Original post by Gome44)
λe^-x is not part of the C.F?
Yup, I've got the answer now thanks!

Would you mind giving me a hand on this question

I've got as far as dz/dx = cosx

dy/dx = cosxdy/dx

and I tried to use the product rule to find d^y/dx^2 and I got -sinxdy/dx + cosxd^2y/dx^2 or did I go wrong somewhere?
6. (Original post by creativebuzz)
Yup, I've got the answer now thanks!

Would you mind giving me a hand on this question

I've got as far as dz/dx = cosx

dy/dx = cosxdy/dx

and I tried to use the product rule to find d^y/dx^2 and I got -sinxdy/dx + cosxd^2y/dx^2 or did I go wrong somewhere?
This part in bold is incorrect. , so what you should end up with is

You then need to use implicit differentiation

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