I have a 2 coupled non-linear ODEs that make up a Differential Algebraic Equation. $$V' = -\frac{V}{2\delta}\delta ' - \frac{6}{\delta ^2 } + \frac{6}{V}\Delta T$$ $$\delta ' = \frac{6}{\delta V}-\frac{\delta}{V}V'$$ where the prime denoted differentiation wrt y. I need to integrate these from $y=0$ to $y=H$ with the conditions: $$V(y=H)=0, \delta (y=H)=0$$ I am using MATLABs ODE15i to solve them and using a root solver to find consistent initial conditions for : $$V'(y=H), \delta '(y=H)$$ I am pretty certain that everything I have done is correct since I can easily solve these equation by integrating from H to 0 instead.
I have tried to implement the shooting method so I can solve this by integrating from $0$ to $H$ but it has not worked.
What I have tried is to use two initial guesses for V and $\delta$ at y=0 and find consistent initial conditions for V' and $\delta '$ and solve in an iteration where each guess for V and $\delta$ is updated with the secant method. My solution does not converge.
Please any suggestions or help on how to solve this problem would really be appreciated.