Internal problem ID [9305]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 6, non-linear second order
Problem number: 1726.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]]
Solve \begin {gather*} \boxed {y^{\prime \prime } \left (x -y\right )-h \left (y^{\prime }\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.009 (sec). Leaf size: 39
dsolve(diff(diff(y(x),x),x)*(x-y(x))-h(diff(y(x),x))=0,y(x), singsol=all)
\[ y \relax (x ) = x +\RootOf \left (-x +\int _{}^{\textit {\_Z}}\frac {1}{-1+\RootOf \left (\int _{}^{\textit {\_Z}}\frac {\textit {\_a} -1}{h \left (\textit {\_a} \right )}d \textit {\_a} +\ln \left (-\textit {\_g} \right )+c_{1}\right )}d \textit {\_g} +c_{2}\right ) \]
✓ Solution by Mathematica
Time used: 0.198 (sec). Leaf size: 82
DSolve[-h[y'[x]] + (x - y[x])*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\left \{x=\int \frac {\exp \left (-\int _1^{K[4]}\frac {K[3]-1}{h(K[3])}dK[3]-c_1\right )}{h(K[4])} \, dK[4]+c_2,y(x)=x-\exp \left (-\int _1^{K[4]}\frac {K[3]-1}{h(K[3])}dK[3]-c_1\right )\right \},\{y(x),K[4]\}\right ] \]