60.7.136 problem 1727 (book 6.136)

Internal problem ID [11725]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 6, non-linear second order
Problem number : 1727 (book 6.136)
Date solved : Tuesday, January 28, 2025 at 06:11:16 PM
CAS classification : [[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]]

\begin{align*} y^{\prime \prime } \left (x -y\right )-h \left (y^{\prime }\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.011 (sec). Leaf size: 39

dsolve(diff(diff(y(x),x),x)*(x-y(x))-h(diff(y(x),x))=0,y(x), singsol=all)
 

\[ y = x +\operatorname {RootOf}\left (-x +\int _{}^{\textit {\_Z}}\frac {1}{-1+\operatorname {RootOf}\left (\int _{}^{\textit {\_Z}}\frac {\textit {\_a} -1}{h \left (\textit {\_a} \right )}d \textit {\_a} +\ln \left (-\textit {\_g} \right )+c_{1} \right )}d \textit {\_g} +c_{2} \right ) \]

✓ Solution by Mathematica

Time used: 0.171 (sec). Leaf size: 82

DSolve[-h[D[y[x],x]] + (x - y[x])*D[y[x],{x,2}] == 0,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\left \{x=\int \frac {\exp \left (-\int _1^{K[4]}\frac {K[3]-1}{h(K[3])}dK[3]-c_1\right )}{h(K[4])} \, dK[4]+c_2,y(x)=x-\exp \left (-\int _1^{K[4]}\frac {K[3]-1}{h(K[3])}dK[3]-c_1\right )\right \},\{y(x),K[4]\}\right ] \]