Question

I need some serious help with this U-sub Differential equation

Answer 1

\[y^\prime -y =e ^{-x}y^2\]

Answer 2

Divide by y^2 to get
\[y^{-2}y'-y^{-1}=e^{-x}\]
then let \[u=y^{-1}\]
\[u'=-y^{-2}y' \mbox{ (chain rule)}\]
substituting this into the above equation we get
\[-u' - u=e^{-x}\]
\[u'+u=-e^{-x}\]

Solve for u, and then use u = 1/y to find y

Answer 3

would you not need to take the integral here?

Answer 4

Well it's a basic linear differential equation right now, do you know how to solve these?

Answer 5

Using an integrating factor