Question

Solve the following differential equation:

y' = (y^2-1)/(2t)

Answer 1

separate variables

Answer 2

Yes.

Answer 3

I know how to do it until i got to one point and blanked out.

Answer 4

dy/(y^2-1) = dt/(2t)

Answer 5

Yeah. I then multiplied both sides by 2

Answer 6

for left side,
consider trig substitution \(y = sin \theta\)

Answer 7

But should i multiply both sides by two or it doesn't matter?

Answer 8

it doesnt matter

Answer 9

mmk.

Answer 10

just take the integral both sides by any means thats possible to u..

Answer 11

I'll take it using your way.

Answer 12

Can't i just use ln |y^2-1| as the integrate of the left side?

Answer 13

and the right side be ln |2t|

Answer 14

lets see

Answer 15

\(\large \frac{dy}{y^2-1} = \frac{ dt}{2t} \)

integrate both sides


\(\large \int \frac{dy}{y^2-1} = \int \frac{ dt}{2t} \)

\(\large \int \frac{dy}{y^2-1} = \frac{1}{2}\int \frac{ dt}{t} \)

\(\large \int \frac{dy}{y^2-1} = \frac{1}{2}\ln |t | + c \)

Answer 16

right side, u can pull out constant out of the integral...
u still need to deal wid integrating left side

Answer 17

Right. But wouldnt left side be basically: