Internal problem ID [10174]
Internal file name [OUTPUT/9121_Monday_June_06_2022_06_42_18_AM_10816195/index.tex]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 7, non-linear third and higher order
Problem number: 1852.
ODE order: 4.
ODE degree: 1.
The type(s) of ODE detected by this program : "unknown"
Maple gives the following as the ode type
[[_high_order, _missing_x], [_high_order, _missing_y], [_high_order, _with_linear_symmetries], [_high_order, _reducible, _mu_poly_yn]]
Unable to solve or complete the solution.
Unable to parse ODE.
Maple trace
`Methods for high order ODEs: --- Trying classification methods --- trying 4th order ODE linearizable_by_differentiation trying high order reducible trying differential order: 4; mu polynomial in y -> Calling odsolve with the ODE`, -(5/3)*ln(diff(diff(_b(_a), _a), _a))+ln(diff(diff(diff(_b(_a), _a), _a), _a))+c__1 = 0, _b(_a)` Methods for third order ODEs: --- Trying classification methods --- trying 3rd order ODE linearizable_by_differentiation differential order: 3; trying a linearization to 4th order trying differential order: 3; missing variables `, `-> Computing symmetries using: way = 3 -> Calling odsolve with the ODE`, diff(_g(_f), _f) = _g(_f)^(5/3)*exp(-c__1), _g(_f), HINT = [[1, 0], [_f, -(3/2)*_g]]` *** symmetry methods on request `, `1st order, trying reduction of order with given symmetries:`[1, 0], [_f, -3/2*_g]
✓ Solution by Maple
Time used: 0.141 (sec). Leaf size: 36
dsolve(3*diff(diff(y(x),x),x)*diff(diff(diff(diff(y(x),x),x),x),x)-5*diff(diff(diff(y(x),x),x),x)^2=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= c_{1} x +c_{2} \\ y \left (x \right ) &= 3 \left (c_{2} +x \right ) \sqrt {6}\, c_{1} \sqrt {-\frac {c_{1}}{c_{2} +x}}+c_{3} x +c_{4} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.342 (sec). Leaf size: 28
DSolve[-5*Derivative[3][y][x]^2 + 3*y''[x]*Derivative[4][y][x] == 0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_2 \left (-\sqrt {2 x+3 c_1}\right )+c_4 x+c_3 \]