60.8.5 problem 1841

Internal problem ID [11840]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 7, non-linear third and higher order
Problem number : 1841
Date solved : Monday, January 27, 2025 at 11:43:30 PM
CAS classification : [[_3rd_order, _exact, _nonlinear]]

\begin{align*} x^{2} y^{\prime \prime \prime }+x y^{\prime \prime }+\left (2 y x -1\right ) y^{\prime }+y^{2}-f \left (x \right )&=0 \end{align*}

✗ Solution by Maple

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

Not solved