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. $\displaystyle C1x^2+C2$

2. $\displaystyle C1lnt+C2+t^2$

3. $\displaystyle [C1+C2^{e^t}]^{1/2}$

4.$\displaystyle C1 tan(C1t+C2)$