60.7.225 problem 1816 (book 6.225)

Internal problem ID [11814]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 6, non-linear second order
Problem number : 1816 (book 6.225)
Date solved : Monday, January 27, 2025 at 11:37:44 PM
CAS classification : [NONE]

\begin{align*} h \left (y\right ) y^{\prime \prime }-D\left (h \right )\left (y\right ) {y^{\prime }}^{2}-h \left (y\right )^{2} j \left (x , \frac {y^{\prime }}{h \left (y\right )}\right )&=0 \end{align*}

✗ Solution by Maple

dsolve(h(y(x))*diff(diff(y(x),x),x)-D(h)(y(x))*diff(y(x),x)^2-h(y(x))^2*j(x,diff(y(x),x)/h(y(x)))=0,y(x), singsol=all)
 

\[ \text {No solution found} \]

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

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

Not solved