60.7.34 problem 1624 (6.34)

Internal problem ID [11623]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 6, non-linear second order
Problem number : 1624 (6.34)
Date solved : Monday, January 27, 2025 at 11:27:45 PM
CAS classification : [NONE]

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

✗ Solution by Maple

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

\[ \text {No solution found} \]

✗ Solution by Mathematica

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

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

Not solved