Solving dy/dx = 6xy/(3-x²) by separation of variables

[SteliosVas]

Homework Statement

The problem is Solve the following differential equation: dy/dx = 6*x*y/(3-x^2)

Homework Equations

Okay so I know the first step is integrating both sides and separating the variables

The Attempt at a Solution

So separating the variables and integrating I get integral of \int y*dy \ = integral of
\int (6x)/(3-x^2) \, dx

Using substation for the the x variable I get -3ln(-x^2+3) +c and for the y variable as just y(x).

Now after this what is the next step. Should i rewrite the log natural as 1/(x^2-3)^2?

 

[Simon Bridge]

Now after this what is the next step.

Stop - you are there. Put LHS = RHS.

for the y variable as just y(x).

But $\int y\;dy \neq y$

 

[Mark44]

Homework Statement

The problem is Solve the following differential equation: dy/dx = 6*x*y/(3-x^2)

Homework Equations

Okay so I know the first step is integrating both sides and separating the variables

Separate the variables first before integrating.

The Attempt at a Solution

So separating the variables and integrating I get integral of \int y*dy \ = integral of
\int (6x)/(3-x^2) \, dx

Check your algebra. The left side is NOT y * dy.

Using substation for the the x variable I get -3ln(-x^2+3) +c and for the y variable as just y(x).

Now after this what is the next step. Should i rewrite the log natural as 1/(x^2-3)^2?

You have a mistake in here as well.