1. ## nonlinear second order

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
1. $C1x^2+C2$
2. $C1lnt+C2+t^2$
3. $[C1+C2^{e^t}]^{1/2}$
4. $C1 tan(C1t+C2)$

2. 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.

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

4. 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!