Internal problem ID [9370]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 6, non-linear second order
Problem number: 1792 (book 6.201).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {\left (1-y\right ) y^{\prime \prime }-3 \left (1-2 y\right ) \left (y^{\prime }\right )^{2}-h \relax (y)=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 90
dsolve((1-y(x))*diff(diff(y(x),x),x)-3*(1-2*y(x))*diff(y(x),x)^2-h(y(x))=0,y(x), singsol=all)
\begin{align*} \int _{}^{y \relax (x )}\frac {{\mathrm e}^{-6 \textit {\_b}}}{\sqrt {-2 \left (\int \frac {{\mathrm e}^{-12 \textit {\_b}} h \left (\textit {\_b} \right )}{\left (\textit {\_b} -1\right )^{7}}d \textit {\_b} \right )+c_{1}}\, \left (\textit {\_b} -1\right )^{3}}d \textit {\_b} -x -c_{2} = 0 \\ \int _{}^{y \relax (x )}-\frac {{\mathrm e}^{-6 \textit {\_b}}}{\sqrt {-2 \left (\int \frac {{\mathrm e}^{-12 \textit {\_b}} h \left (\textit {\_b} \right )}{\left (\textit {\_b} -1\right )^{7}}d \textit {\_b} \right )+c_{1}}\, \left (\textit {\_b} -1\right )^{3}}d \textit {\_b} -x -c_{2} = 0 \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.499 (sec). Leaf size: 168
DSolve[-h[y[x]] - 3*(1 - 2*y[x])*y'[x]^2 + (1 - y[x])*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}-\frac {e^{\frac {1}{2} (12-12 K[2])}}{(K[2]-1)^3 \sqrt {c_1+2 \int _1^{K[2]}-\frac {\exp (-2 (6 (K[1]-1)+3 \log (K[1]-1))) h(K[1])}{K[1]-1}dK[1]}}dK[2]\&\right ][x+c_2] \\ y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {e^{\frac {1}{2} (12-12 K[3])}}{(K[3]-1)^3 \sqrt {c_1+2 \int _1^{K[3]}-\frac {\exp (-2 (6 (K[1]-1)+3 \log (K[1]-1))) h(K[1])}{K[1]-1}dK[1]}}dK[3]\&\right ][x+c_2] \\ \end{align*}