The question is, "Solve the initial value problem $2y\frac{dy}{dx}+4=y^2+4x$ with $y(0)=5$.
a. To solve this, we should use the substitution u= ____________ With this substitution, y = ______________ y'= ______________
After the substitution from the previous part, we obtain the following linear differential equation in x, u, u':
The solution to the original initial value problem is described by the following equation in x,y
My professor did not go over any questions like this and I am having trouble understanding what I need to do for any part of this. Any help would be greatly appreciated!
$2y\frac{dy}{dx}+4=y^2+4x$ with $y(0)=5$. Put $u=y^2$ then $\frac{du}{dx}=2y\frac{dy}{dx}$. This gives $\frac{du}{dx}+4=u+4x$ or $\frac{du}{dx}-u=4x-4$ (linear ODE). Can you take it from here?