60.7.161 problem 1752 (book 6.161)

Internal problem ID [11750]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 6, non-linear second order
Problem number : 1752 (book 6.161)
Date solved : Monday, January 27, 2025 at 11:33:59 PM
CAS classification : [NONE]

\begin{align*} 4 y^{\prime \prime } y-3 {y^{\prime }}^{2}+\left (6 y^{2}-\frac {2 f^{\prime }\left (x \right ) y}{f \left (x \right )}\right ) y^{\prime }+y^{4}-2 y^{2} y^{\prime }+g \left (x \right ) y^{2}+f \left (x \right ) y&=0 \end{align*}

✗ Solution by Maple

dsolve(4*diff(diff(y(x),x),x)*y(x)-3*diff(y(x),x)^2+(6*y(x)^2-2*diff(f(x),x)/f(x)*y(x))*diff(y(x),x)+y(x)^4-2*y(x)^2*diff(y(x),x)+g(x)*y(x)^2+f(x)*y(x)=0,y(x), singsol=all)
 

\[ \text {No solution found} \]

✗ Solution by Mathematica

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

DSolve[f[x]*y[x] + g[x]*y[x]^2 + y[x]^4 - 2*y[x]^2*D[y[x],x] + (6*y[x]^2 - (2*y[x]*Derivative[1][f][x])/f[x])*D[y[x],x] - 3*D[y[x],x]^2 + 4*y[x]*D[y[x],{x,2}] == 0,y[x],x,IncludeSingularSolutions -> True]
 

Not solved