# Help Solving a differential equation

Hello, i was wondering if someone can help me along with solving this differential equation.

(x+2y)y'=y

I believe you use substitution. Right now I am setting my substitution to
v=(x+2y), but then when i follow through with my work, it doesn't simplify down to a seperable or first order linear equation. Am I doing something wrong?

-giuseppe

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try this should make a nice linear in terms of x

divide the left side by y

then divide 1 by y' and you should end up with a linear in terms of x

Rewrite this in the form M(x,y)dx + N(x,y)dy = 0. Then, check if this is an exact differential equation. If not, can you find an integrating factor to make it exact?

I don't think substitution works here. It's just not separable.

HallsofIvy
Homework Helper
This is NOT an exact equation either.

I like Valhalla's suggestion. You can rewrite it as

y(dx/dy)= x+ 2y which is a LINEAR equation for x as a function of y. If you really need y as a function of x, invert the function.

I didn't say it was exact... I said he should check if it was exact. It's easy enough to make it exact with an integrating factor though.

There is more than one way to skin a cat...