Solve the differential equation dy/dt = y^2 / (4-t^2)^(1/2)

1/sin-1(t) + c
1/sin-1(t/2) + c
2/sin-1(t/2) + c
2/tan-1(t/2) + c

Question

Solve the differential equation dy/dt = y^2 / (4-t^2)^(1/2)

1/sin-1(t) + c
1/sin-1(t/2) + c
2/sin-1(t/2) + c
2/tan-1(t/2) + c

kc_kennylau · Answer

Put the terms with y on one side and terms with t on another.

anonymous · Answer

Ok, then what?
dy/y^2=dt/(4-t^2)^(1/2)

kc_kennylau · Answer

integrate both sides

kc_kennylau · Answer

$$\int\frac{dy}{y^2}=\int\frac{dt}{\sqrt{4-t^2}}$$

kc_kennylau · Answer

http://www.wolframalpha.com/input/?i=int+1%2Fsqrt%284-t%5E2%29

anonymous · Answer

that's not an answer though?

kc_kennylau · Answer

I'd never give you the answer

kc_kennylau · Answer

You have to find it out yourself

anonymous · Answer

I'm confused. If you integrate both sides, then you'd get sin-1(t/2). Which isn't a choice?

kc_kennylau · Answer

Because the left hand side is still not calculated

anonymous · Answer

oh! okay. i see. the left side would be -1/y. 
so it'd be -1/y=arcsin(t/2) + c
you multiple both sides by y then divide both sides by arcsin(t/2) + c. 
so you get
-1/arcsin(t/2) + c

...but that's still not answer choice, right?

kc_kennylau · Answer

well,,,

anonymous · Answer

did i do something wrong?

kc_kennylau · Answer

Don't think so