# Non-Linear and non separable differential equation

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• Jun 8th 2011, 07:51 PM
metalkakkarot
Non-Linear and non separable differential equation
How can i solve this equation as it is non-linear and non seperable, i cant use the integrating factor as Q(x) does not exist and i cant seperate so that x and y are separate.

x.(dy/dx)=-3y + 6x

some tips please
• Jun 8th 2011, 08:01 PM
Chris L T521
Quote:

Originally Posted by metalkakkarot
How can i solve this equation as it is non-linear and non seperable, i cant use the integrating factor as Q(x) does not exist and i cant seperate so that x and y are separate.

x.(dy/dx)=-3y + 6x

some tips please

What do you mean its not linear? Note that $x\frac{\,dy}{\,dx}=-3y+6x \implies \frac{\,dy}{\,dx}+\frac{3}{x}y=6$ is of the form $\frac{\,dy}{\,dx}+P(x)y=Q(x)$, which is clearly linear...

Can you take it from here and use the integrating factor?
• Jun 8th 2011, 08:09 PM
metalkakkarot
thanks..got it now
i used this before and got the wrong answer..

integrating factor is e^3lnx
got answer as y=(3/2)x +c/(x^3)

which is correct

thankyou very much :)