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henpen
\[ y\ddot{y}-\dot{y}^2=1\]
\[ y\ddot{y}-\dot{y}^2=1\]
The boundary conditions are \[ y(a)=y(-a)=1\] . \[ \large \ddot{y}=\frac{ \dot{y}^2+1}{y} \] Let \[ p=\dot{y}\] . \[ \large \dot{p}=\frac{dp}{dy}p=\frac{ p^2+1}{y}\] \[ \large\int \frac{p}{p^2+1}dp= \int \frac{1}{y}dy\] Let \[ u=p^2\] \[ \large \frac{1}{2}ln|u+1| =ln|\sqrt{u+1}|=ln|y|+c\] \[ \large \sqrt{u+1} =ky\] \[ \large \dot{y}^2+1 =by^2\] What do I do now?
after this dy/dx = sqrt(by2-1) and then proceed ...