MHB 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]

 

[chisigma]

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]

I'm not surprised because that is the natural consequence of ...

http://mathhelpboards.com/differential-equations-17/need-help-solving-2nd-order-nonlinear-differential-equation-12222.html#post58240

Unfortunately the 'direct attack' to the ODE...

$\displaystyle y^{\ '} = \sqrt{a\ y^{4} - (1 + a) y^{2} + 1}\ (1)$

... leads to an elliptic integral, a rather indigestible dish:( ... but never say never again!...

By the way, welcome to MHB! :)...

Kind regards

$\chi$ $\sigma$