# Simple Differential Equation

1. Oct 7, 2014

### SteliosVas

1. The problem statement, all variables and given/known data

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

2. Relevant equations

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

3. 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?

2. Oct 7, 2014

### Simon Bridge

Stop - you are there. Put LHS = RHS.
But $\int y\;dy \neq y$

3. Oct 7, 2014

### Staff: Mentor

Separate the variables first before integrating.
Check your algebra. The left side is NOT y * dy.
You have a mistake in here as well.

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