Internal problem ID [9947]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 6, non-linear second order
Problem number: 1624 (6.34).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [NONE]
\[ \boxed {y^{\prime \prime }+y^{\prime } y-y^{3}-\left (\frac {f^{\prime }\left (x \right )}{f \left (x \right )}+f \left (x \right )\right ) \left (3 y^{\prime }+y^{2}\right )+\left (f \left (x \right )^{2} a +3 f^{\prime }\left (x \right )+\frac {3 {f^{\prime }\left (x \right )}^{2}}{f \left (x \right )^{2}}-\frac {f^{\prime \prime }\left (x \right )}{f \left (x \right )}\right ) y=-b f \left (x \right )^{3}} \]
✗ 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: 0.0 (sec). Leaf size: 0
DSolve[b*f[x]^3 - y[x]^3 + y[x]*y'[x] - (f[x] + Derivative[1][f][x]/f[x])*(y[x]^2 + 3*y'[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]) + y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
Not solved