First Order Nonlinear Differential Equation!

[frank1234]

Hi, I need help solving this ode, when I try to solve it I end up with a big crazy answer and I believe it should be simpler.

(dy/dx)^2=((ay^4)/2)-(a+1)y^2+1

y(0)=0, y'(0)=1 and a is within [0,1]

 

[stapel]

Hi, I need help solving this ode, when I try to solve it I end up with a big crazy answer and I believe it should be simpler.

What were your steps? What did you end up with? Thank you!

 

[HallsofIvy]

I don't see any reason why 'it should be simpler'! You can factor that "quadratic in \(\displaystyle y^2\)" but it isn't going to give any simple results