# differentiable equation problem!

• Feb 11th 2009, 09:33 PM
khood
differentiable equation problem!
Solve the differential equation below by making the change of variable u = y/x. (Use K to represent any constant and place "+" before it.) http://www.webassign.net/www14/symIm...1451513cf6.gif

so when you replaced with u, you get dy/dx = u + e^(5u)

how do you solve that since you still have dy/dx and not a du..?
• Feb 11th 2009, 09:57 PM
Chris L T521
Quote:

Originally Posted by khood
Solve the differential equation below by making the change of variable u = y/x. (Use K to represent any constant and place "+" before it.) http://www.webassign.net/www14/symIm...1451513cf6.gif

so when you replaced with u, you get dy/dx = u + e^(5u)

how do you solve that since you still have dy/dx and not a du..?

Since $\displaystyle u=\frac{y}{x}\implies y=ux$, we see that $\displaystyle \frac{\,dy}{\,dx}=u+x\frac{\,du}{\,dx}$ (by product rule)

Thus, the DE becomes $\displaystyle x\frac{\,du}{\,dx}+u=u+e^{5u}\implies x\frac{\,du}{\,dx}=e^{5u}$. Now apply the technique of separation of variables.

Can you take it from here?