Internal problem ID [9264]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 6, non-linear second order
Problem number: 1686 (book 6.95).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [NONE]
Solve \begin {gather*} \boxed {2 \left (-x^{k}+4 x^{3}\right ) \left (y^{\prime \prime }+y^{\prime } y-y^{3}\right )-\left (k \,x^{k -1}-12 x^{2}\right ) \left (3 y^{\prime }+y^{2}\right )+y a x +b=0} \end {gather*}
✗ Solution by Maple
dsolve(2*(-x^k+4*x^3)*(diff(diff(y(x),x),x)+y(x)*diff(y(x),x)-y(x)^3)-(k*x^(k-1)-12*x^2)*(3*diff(y(x),x)+y(x)^2)+y(x)*a*x+b=0,y(x), singsol=all)
\[ \text {No solution found} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[b + a*x*y[x] - (-12*x^2 + k*x^(-1 + k))*(y[x]^2 + 3*y'[x]) + 2*(4*x^3 - x^k)*(-y[x]^3 + y[x]*y'[x] + y''[x]) == 0,y[x],x,IncludeSingularSolutions -> True]
Not solved