60.7.36 problem 1626 (6.36)

Internal problem ID [11625]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 6, non-linear second order
Problem number : 1626 (6.36)
Date solved : Monday, January 27, 2025 at 11:27:47 PM
CAS classification : [[_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]]

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

✗ Solution by Maple

dsolve(diff(diff(y(x),x),x)+2*y(x)*diff(y(x),x)+f(x)*diff(y(x),x)+diff(f(x),x)*y(x)=0,y(x), singsol=all)
 

\[ \text {No solution found} \]

✗ Solution by Mathematica

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

DSolve[y[x]*D[ f[x],x] + f[x]*D[y[x],x] + 2*y[x]*D[y[x],x] + D[y[x],{x,2}] == 0,y[x],x,IncludeSingularSolutions -> True]
 

Not solved