- #1
aximus
Homework Statement
Solve this IVP:
y'=(y-9x)^2 ; y(0)=1
Given a hint: Use the substitution v=y-9x and partial fractions.
Homework Equations
...
The Attempt at a Solution
I was able to solve this DE through partial fractions, etc until I ended up at this point
ln (v-3/v+3) = 6x+C
or
(v-3)/(v+3) = Ae^6x (where A = e^C)
I won't show my entire working (unless requested) as the partial fractions and simplification is lengthy, but I know I am correct up to this point as the answers get to this point and then just tell me to use some simple algebraic rearranging to get:
y=9x-v=3(A*exp(6x)+1)/(1-A*exp(6x))
So yeah, I am stuck at manipulating this fraction about and to solve for v (and then y). I'm sure that this involves a very quick manipulation I should know, but it is really bothering me.
Thank you for your help.