60.7.88 problem 1679 (book 6.88)

Internal problem ID [11677]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 6, non-linear second order
Problem number : 1679 (book 6.88)
Date solved : Tuesday, January 28, 2025 at 06:07:23 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }-\sqrt {a \,x^{2} {y^{\prime }}^{2}+b y^{2}}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.173 (sec). Leaf size: 64

dsolve(x^2*diff(diff(y(x),x),x)-(a*x^2*diff(y(x),x)^2+y(x)^2*b)^(1/2)=0,y(x), singsol=all)
 

\begin{align*} y &= 0 \\ y-{\mathrm e}^{\int _{}^{\ln \left (x \right )}\operatorname {RootOf}\left (-y \left (\int _{}^{\textit {\_Z}}\frac {1}{y \textit {\_a}^{2}-\textit {\_a} y-\sqrt {y^{2} \left (a \,\textit {\_a}^{2}+b \right )}}d \textit {\_a} \right )-\textit {\_b} +c_{1} \right )d \textit {\_b} +c_{2}} &= 0 \\ \end{align*}

✗ Solution by Mathematica

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

DSolve[-Sqrt[b*y[x]^2 + a*x^2*D[y[x],x]^2] + x^2*D[y[x],{x,2}] == 0,y[x],x,IncludeSingularSolutions -> True]
 

Not solved