Find the specific solution for the following differential equations:
a) (dy/dx)^2 - x^4 = 0 given the initial value y(1) = 0
b) dy/dx = ysinx given the initial value y(pi) = 1
Rearrange to get $\displaystyle \frac{\,dy}{\,dx}=x^2$
This should be easy enough to solve now...
Apply separation of variables to get $\displaystyle \frac{\,dy}{y}=\sin x\,dx$b) dy/dx = ysinx given the initial value y(pi) = 1
Now integrate both sides and then solve for y.
In both of these, apply the initial condition after you have integrated and solved for y. This will help you determine the value of the arbitrary constant $\displaystyle C$.
--Chris