60.7.95 problem 1686 (book 6.95)

Internal problem ID [11684]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 6, non-linear second order
Problem number : 1686 (book 6.95)
Date solved : Monday, January 27, 2025 at 11:29:56 PM
CAS classification : [NONE]

\begin{align*} 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 )+a x y+b&=0 \end{align*}

✗ 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: 0.000 (sec). Leaf size: 0

DSolve[b + a*x*y[x] - (-12*x^2 + k*x^(-1 + k))*(y[x]^2 + 3*D[y[x],x]) + 2*(4*x^3 - x^k)*(-y[x]^3 + y[x]*D[y[x],x] + D[y[x],{x,2}]) == 0,y[x],x,IncludeSingularSolutions -> True]
 

Not solved