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Solved by finding the first integral directly
Introduction
ode of the form \(y^{\prime \prime }+a_{2}\left ( x,y\right ) \left ( y^{\prime }\right ) ^{2}+a_{1}\left ( x,y\right ) y^{\prime }+a_{0}\left ( x,y\right ) =0\)

ode internal name "exact_nonlinear_second_order_ode_using_first_integral"

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