Question

Find all solutions of (x^2)(y)(y')=(y^2-1)^(3/2).

Answer 1

@ganeshie8

Answer 2

separable

Answer 3

I got (x^2)*dy/dx=(y^2-1)^(3/2) divided by y, but what's next?

Answer 4

next separate the variables :
arrange all the y terms on dy side and x terms on dx side

Answer 5

\[\large \begin{align}\\ x^2y\dfrac{dy}{dx}& =(y^2-1)^{3/2} \end{align}\]

Answer 6

\[\large \begin{align}\\ x^2y\dfrac{dy}{dx}& =(y^2-1)^{3/2} \\~\\
\dfrac{ydy}{(y^2-1)^{3/2} }& =\dfrac{dx}{x^2}\\~\\

\end{align}\]

Answer 7

integrate ^^

Answer 8

How do I integrate y*dy/(y^2-1)^(3/2)?

Answer 9

u-substitution?

Answer 10

yes :)

Answer 11

So I got -1/(sqrt(y^2-1))=-1/x+C, how do I solve for y?

Answer 12

you may leave the answer in implicit form, don't need to solve it explicitly unless you're asked to do so

Answer 13

I got sqrt(y^2-1)=x-1/c, am I right?

Answer 14

1/(sqrt(y^2-1))=1/x+C

maybe leave it like this

Answer 15

if you flip it, you would get :

sqrt(y^2-1) = x/(1+Cx)

Answer 16

Thank you!