60.7.167 problem 1758 (book 6.167)

Internal problem ID [11756]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 6, non-linear second order
Problem number : 1758 (book 6.167)
Date solved : Monday, January 27, 2025 at 11:34:14 PM
CAS classification : [NONE]

\begin{align*} a y y^{\prime \prime }-\left (a -1\right ) {y^{\prime }}^{2}+\left (a +2\right ) f \left (x \right ) y^{2} y^{\prime }+f \left (x \right )^{2} y^{4}+a f^{\prime }\left (x \right ) y^{3}&=0 \end{align*}

✗ Solution by Maple

dsolve(a*y(x)*diff(diff(y(x),x),x)-(a-1)*diff(y(x),x)^2+(a+2)*f(x)*y(x)^2*diff(y(x),x)+f(x)^2*y(x)^4+a*diff(f(x),x)*y(x)^3=0,y(x), singsol=all)
 

\[ \text {No solution found} \]

✗ Solution by Mathematica

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

DSolve[f[x]^2*y[x]^4 + (2 + a)*f[x]*y[x]^2*D[y[x],x] + a*y[x]^3*D[y[x],x] - (-1 + a)*D[y[x],x]^2 + a*y[x]*D[y[x],{x,2}] == 0,y[x],x,IncludeSingularSolutions -> True]
 

Not solved