# Thread: Second Order ODE: Exact Equations

1. ## Second Order ODE: Exact Equations

The problem is
y+(x+2xy^2)dy/dx=0
I’m trying to find an integrating factor to make this exact. To get the integrating factor “u”:
du/dy=u[(Nx-My)/M ]= u(1+2y2-1)/y=2y*u
u=e^(2y)
If I multiply it by My and Nx, they don't equal.
Then my equation still isn’t exact. What did I do wrong? I feel like I’ve been over this 20 times already.

2. I have a question. Fom what you have

$\displaystyle y +\left(x + 2xy^2\right) \dfrac{dy}{dx} = 0$. Isn't this ODE spearable?

3. Originally Posted by sweetscissor
The problem is
y+(x+2xy^2)dy/dx=0
I’m trying to find an integrating factor to make this exact. To get the integrating factor “u”:
du/dy=u[(Nx-My)/M ]= u(1+2y2-1)/y=2y*u
u=e^(2y)
If I multiply it by My and Nx, they don't equal.
Then my equation still isn’t exact. What did I do wrong? I feel like I’ve been over this 20 times already.
To comment on what you've done - check your integration

$\displaystyle \left(\int 2y\,dy = y^2\right)$