nonlinear second order

**wopashui** · Nov 4th 2010, 10:07 AM

I know we can use the subsittion of m = y' for 1 and 2, then let y'=m(y(t))for 3 and 4, but I have a hard time to solve for the answer

as the answers are given, can anyone show me the setps, I need to undertsand this for the test tomorrow

the question is inside the image and
tha answers are
1. $C1x^2+C2$
2. $C1lnt+C2+t^2$
3. $[C1+C2^{e^t}]^{1/2}$
4. $C1 tan(C1t+C2)$

**Ackbeet** · Nov 4th 2010, 10:41 AM

As you've indicated, reduce the order for 1 and 2. For 3, note that (yy')' = LHS. Then integrate. For 4, just integrate directly once. You'll get a first-order separable equation out of that.

**wopashui** · Nov 4th 2010, 10:46 AM

I did that, but for some reason i can't get the right answer, can you show me the steps if possible?

**Ackbeet** · Nov 4th 2010, 10:48 AM

can you show me the steps if possible?

No, but if you show your work, I'll comment on it. Please distinguish the problems and label clearly. Thanks!

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