Hello all,
I'm trying to solve the following second order non linear differential equation:
\(\displaystyle 0 = A_{1} (J'(x_{t}))^{\frac{\alpha-1}{\alpha}} + A_{2} x_{t}^{2-\frac{1}{\beta}} J'(x_{t}) + A_{3} x_{t}^{2} J''(x_{t}) \)
The constants \(\displaystyle \alpha\) and \(\displaystyle \beta\) can be related if needed for solution.
We know that \(\displaystyle x(0)=x_{0}\) is known and \(\displaystyle J(x_{T})=K(x_{T})\), where the function \(\displaystyle K(x_{T})\) is known.
This equation can be solved numerically, but before doing that, i need to know if it can be reduced somehow in order to get an analytical solution.
Do you have any ideas?
Thank you so much,
A.
I'm trying to solve the following second order non linear differential equation:
\(\displaystyle 0 = A_{1} (J'(x_{t}))^{\frac{\alpha-1}{\alpha}} + A_{2} x_{t}^{2-\frac{1}{\beta}} J'(x_{t}) + A_{3} x_{t}^{2} J''(x_{t}) \)
The constants \(\displaystyle \alpha\) and \(\displaystyle \beta\) can be related if needed for solution.
We know that \(\displaystyle x(0)=x_{0}\) is known and \(\displaystyle J(x_{T})=K(x_{T})\), where the function \(\displaystyle K(x_{T})\) is known.
This equation can be solved numerically, but before doing that, i need to know if it can be reduced somehow in order to get an analytical solution.
Do you have any ideas?
Thank you so much,
A.