Unable to solve a nonlinear DE analytically help needed

[motavassely]

Hi all,

I have a nonlinear differential equation and I need to find an analytic solution for it. Here it is:

\ddot{S}=-{1 \over 6} \dot{S}-{2 \over 7}(1-S)^2(- \dot{S})^{1.3}

I have used a transformation to simplify it:

-\dot S = v

and came up with this DE which I couldn't solve it:

{{dv} \over {dS}} ={1 \over 6} - {2 \over 7} (1-S)^2 v ^ {0.3}

Anyone who can solve them?

Bests,

Ali

 

[balaonspace]

shouldnt you have

{{dv} \over {dS}} ={1 \over 6}v - {2 \over 7} (1-S)^2 v ^ {0.3}

 

[motavassely]

Unfortunately not. It's not a Bernoulli? DE.

 

[jackmell]

Hi all,

I need to find an analytic solution for it.

S(t)=k

 

[motavassely]

a bit more sophisticated solution, please!