Internal problem ID [10168]
Internal file name [OUTPUT/9115_Monday_June_06_2022_06_41_16_AM_33760887/index.tex]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 7, non-linear third and higher order
Problem number: 1846.
ODE order: 3.
ODE degree: 1.
The type(s) of ODE detected by this program : "unknown"
Maple gives the following as the ode type
[[_3rd_order, _missing_x]]
Unable to solve or complete the solution.
Unable to parse ODE.
Maple trace
`Methods for third order ODEs: --- Trying classification methods --- trying a quadrature checking if the LODE has constant coefficients <- constant coefficients successful Methods for first order ODEs: --- Trying classification methods --- trying a quadrature trying 1st order linear <- 1st order linear successful`
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 28
dsolve(2*diff(y(x),x)*diff(diff(diff(y(x),x),x),x)-3*diff(y(x),x)^2=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= c_{1} +c_{2} {\mathrm e}^{\frac {\sqrt {6}\, x}{2}}+c_{3} {\mathrm e}^{-\frac {\sqrt {6}\, x}{2}} \\ y \left (x \right ) &= c_{1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.119 (sec). Leaf size: 57
DSolve[-3*y'[x]^2 + 2*y'[x]*Derivative[3][y][x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 \\ y(x)\to \sqrt {\frac {2}{3}} e^{-\sqrt {\frac {3}{2}} x} \left (c_1 e^{\sqrt {6} x}-c_2\right )+c_3 \\ y(x)\to c_1 \\ \end{align*}