Chapter 4
Nonlinear second order ode
4.1 Exact nonlinear second order ode \(F\left ( x,y,y^{\prime },y^{\prime \prime }\right ) =0\) (Approach 1)
4.2 Exact nonlinear second order ode \(F\left ( x,y,y^{\prime },y^{\prime \prime }\right ) =0\) (Approach 2)
4.3 nonlinear and not exact second order ode
4.4 Solved by finding the first integral directly
4.5 ode of the form \(y^{\prime \prime }+a_{2}\left ( x,y\right ) \left ( y^{\prime }\right ) ^{2}+a_{1}\left ( x,y\right ) y^{\prime }+a_{0}\left ( x,y\right ) =0\)
4.6 ode is Integrable as given
4.7 ode can be made Integrable \(F\left ( x,y,y^{\prime \prime }\right ) =0\)
4.8 Solved using Mainardi Liouville method
4.9 nonlinear second order ode with missing \(x\) or missing \(y\left ( x\right ) \)
4.10 Higher degree second order ode