Internal problem ID [9022]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1443.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+\frac {f^{\prime }\relax (x ) y^{\prime }}{2 f \relax (x )}+\frac {g \relax (x ) y}{f \relax (x )}=0} \end {gather*}
✗ 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: 0.0 (sec). Leaf size: 0
DSolve[y''[x] == -((g[x]*y[x])/f[x]) - (Derivative[1][f][x]*y'[x])/(2*f[x]),y[x],x,IncludeSingularSolutions -> True]
Not solved