Diff Eq w/ Initial Value problem

[shane18]

Here is the problem: {(dy/dx)+(x(y+1)^2)/(y(x+1)^2)=0, y(0)=0}

I have separated and integrated using partial fractions, which gives:

ln|y+1| + 1/(y+1) = ln|x+1| + 1/(x+1) + Constant

Maybe I've been at this for too long, but I can't figure out how to solve for y to determine my constant...

 

[shane18]

Oops! The r.h.s. is negative. Sorry for wasting anyone's time. It appears I cannot solve it explicitly for y, but correcting the signs gives:

ln|y+1| + 1/(y+1) = - ln|x+1| - 1/(x+1) + C

ln|y+1| + 1/(y+1) + ln|x+1| + 1/(x+1) = C

for y(0)=0, ln|1| + 1 + ln|1| + 1 = C

1 + 1 = C = 2

so, ln|y+1| + 1/(y+1) + ln|x+1| + 1/(x+1) = 2

 

[DrPhil]

Here is the problem: {(dy/dx)+(x(y+1)^2)/(y(x+1)^2)=0, y(0)=0}

I have separated and integrated using partial fractions, which gives:

ln|y+1| + 1/(y+1) = ln|x+1| + 1/(x+1) + Constant

Maybe I've been at this for too long, but I can't figure out how to solve for y to determine my constant...

You don't have to "solve for y." Just plug in x=0 and y=0, and solve for C.