- #1
dchau503
- 13
- 0
Homework Statement
[tex] x \frac{du}{dx} \ = \ (u-x)^3 + u[/tex]
solve for u(x) and use [tex] u(1) \ = \ 10[/tex] to solve for u without a constant.
Homework Equations
The given hint is to let [itex]v=u-x[/itex]
The Attempt at a Solution
This equation is not separable and the book wants me to make it separable by a change of variables, i.e.
[tex] u=v+x \ \ \text{and in replacing the original equation with the hint, I get} \frac{du}{dx} = \frac{v^3+u}{x} [/tex].
From [tex]u=v+x, \ \text{I also know that} \frac{du}{dx} \ \text{is also equal to 1, so} \frac{v^3+u}{x} = 1 [/tex]
But this gets rid of all the differentials and I need guidance on how to solve for u in terms of just x.