# Simple Differential Equation

## 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?

## Answers and Replies

Simon Bridge
Homework Helper
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
Mentor

## 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.
SteliosVas said:

## 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.
SteliosVas said:
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.