60.3.437 problem 1443

Internal problem ID [11447]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1443
Date solved : Monday, January 27, 2025 at 11:22:10 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✗ Solution by Maple

dsolve(diff(diff(y(x),x),x) = -1/2*diff(f(x),x)*diff(y(x),x)/f(x)-g(x)/f(x)*y(x),y(x), singsol=all)
 

\[ \text {No solution found} \]

✗ Solution by Mathematica

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

DSolve[D[y[x],{x,2}] == -((g[x]*y[x])/f[x]) - (Derivative[1][f][x]*D[y[x],x])/(2*f[x]),y[x],x,IncludeSingularSolutions -> True]
 

Not solved