First Order Separable Differential equation
I'm in Differential Equations and I have my midterm tomorrow... I can do most everything on my review sheet, but I'm a bit confused when it comes to a very simple initial value problem:
y' = x*y^3, y(0)=1
Here is what I'm doing:
I figure I can use separation of variables like so:
dy/y^3 = x*dx
..and after integrating both sides:
-1/(2*y^2) = (x^2)/2
solving for y gives:
y = 1/x
...which the initial condition y(0) = 1 does not hold.
Can somebody point out what I'm doing wrong? I'm quite confused and I'm running out of time...
Thanks in advance,