Internal problem ID [9981]
Internal file name [OUTPUT/8928_Monday_June_06_2022_05_58_59_AM_17468910/index.tex]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 6, non-linear second order
Problem number: 1660 (book 6.69).
ODE order: 2.
ODE degree: 0.
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.
\[ \boxed {y^{\prime \prime }-y f \left (x , \frac {y^{\prime }}{y}\right )=0} \]
Maple trace
`Methods for second order ODEs: --- Trying classification methods --- trying 2nd order WeierstrassP trying 2nd order JacobiSN differential order: 2; trying a linearization to 3rd order trying 2nd order ODE linearizable_by_differentiation trying 2nd order, 2 integrating factors of the form mu(x,y) -> trying 2nd order, dynamical_symmetries, fully reducible to Abel through one integrating factor of the form G(x,y)/(1+H(x,y)*y)^2 trying 2nd order, integrating factors of the form mu(x,y)/(y)^n, only the singular cases trying symmetries linear in x and y(x) `, `-> Computing symmetries using: way = 3 `, `-> Computing symmetries using: way = exp_sym Try integration with the canonical coordinates of the symmetry [0, y] -> Calling odsolve with the ODE`, diff(_b(_a), _a) = -_b(_a)^2+f(_a, _b(_a)), _b(_a), explicit` *** Sublevel 2 *** Methods for first order ODEs:`
✗ Solution by Maple
dsolve(diff(diff(y(x),x),x)-y(x)*f(x,diff(y(x),x)/y(x))=0,y(x), singsol=all)
\[ \text {No solution found} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[-(f[x, y'[x]/y[x]]*y[x]) + y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
Not solved