Separable differential equation question

[hardyaa1]

I'm new to the separation of variables technique, but I didn't think it was too complicated - all i need to know is whether there is some trick to the following problem, or if I am just supposed to be able to separate the variables by arithmetic... I've spent about an hour and a few pages of paper so far, my math is rusty.

Find, by method of separation of variables, the general solution of the equation: y^2 + 3xy + x^2 - x^2 * dy/dx = 0

Thanks for the help
-Aaron

 

[Deleted member 4993]

I'm new to the separation of variables technique, but I didn't think it was too complicated - all i need to know is whether there is some trick to the following problem, or if I am just supposed to be able to separate the variables by arithmetic... I've spent about an hour and a few pages of paper so far, my math is rusty.

Find, by method of separation of variables, the general solution of the equation: y^2 + 3xy + x^2 - x^2 * dy/dx = 0

Thanks for the help
-Aaron

Make a substitution

y = ux

then

y' = u + xu'

Now the variables can be separated easily.

You are taking a course in ODE - and your math is rusty !!! - all I can say is that polish it up.....