60.7.244 problem 1835 (book 6.244)

Internal problem ID [11833]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 6, non-linear second order
Problem number : 1835 (book 6.244)
Date solved : Monday, January 27, 2025 at 11:43:13 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (y^{2}-x^{2} {y^{\prime }}^{2}+x^{2} y y^{\prime \prime }\right )^{2}-4 x y \left (-y+x y^{\prime }\right )^{3}&=0 \end{align*}

✗ Solution by Maple

dsolve((y(x)^2-x^2*diff(y(x),x)^2+x^2*y(x)*diff(diff(y(x),x),x))^2-4*x*y(x)*(x*diff(y(x),x)-y(x))^3=0,y(x), singsol=all)
 

\[ \text {No solution found} \]

✓ Solution by Mathematica

Time used: 121.011 (sec). Leaf size: 19

DSolve[-4*x*y[x]*(-y[x] + x*D[y[x],x])^3 + (y[x]^2 - x^2*D[y[x],x]^2 + x^2*y[x]*D[y[x],{x,2}])^2 == 0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_1 x e^{\frac {1}{-x+c_2}} \]