3.437 problem 1443

Internal problem ID [9770]
Internal file name [OUTPUT/8712_Monday_June_06_2022_05_18_41_AM_37811089/index.tex]

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.

The type(s) of ODE detected by this program : "unknown"

Maple gives the following as the ode type

[[_2nd_order, _with_linear_symmetries]]

Unable to solve or complete the solution.

\[ \boxed {y^{\prime \prime }+\frac {f^{\prime }\left (x \right ) y^{\prime }}{2 f \left (x \right )}+\frac {g \left (x \right ) y}{f \left (x \right )}=0} \]

Maple trace

`Methods for second order ODEs:`
 

✗ 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