Internal problem ID [10173]
Internal file name [OUTPUT/9120_Monday_June_06_2022_06_42_10_AM_29101823/index.tex]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 7, non-linear third and higher order
Problem number: 1851.
ODE order: 4.
ODE degree: 1.
The type(s) of ODE detected by this program : "unknown"
Maple gives the following as the ode type
[NONE]
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`, diff(diff(diff(diff(y(x), x), x), x), x) = (-(diff(y(x), x))^4*(diff(f(x), x))-(diff(y(x), x))^3*( Integrating factor hint being investigated... trying differential order: 4; exact nonlinear trying differential order: 4; missing variables Trying the formal computation of integrating factors depending on any 2 of [x, y, y, y] differential order: 4; looking for linear symmetries --- Trying Lie symmetry methods, high order --- `, `-> Computing symmetries using: way = 3 `, `-> Computing symmetries using: way = 5`
✗ Solution by Maple
dsolve(diff(y(x),x)*(diff(diff(diff(f(x),x),x),x)*diff(y(x),x)+3*diff(diff(f(x),x),x)*diff(diff(y(x),x),x)+3*diff(f(x),x)*diff(diff(diff(y(x),x),x),x)+f(x)*diff(diff(diff(diff(y(x),x),x),x),x))-diff(diff(y(x),x),x)*f*diff(diff(diff(y(x),x),x),x)+diff(y(x),x)^3*(diff(f(x),x)*diff(y(x),x)+f(x)*diff(diff(y(x),x),x))+2*q(x)*diff(y(x),x)^2*sin(y(x))+(q(x)*diff(diff(y(x),x),x)-diff(q(x),x)*diff(y(x),x))*cos(y(x))=0,y(x), singsol=all)
\[ \text {No solution found} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[2*q[x]*Sin[y[x]]*y'[x]^2 + y'[x]^3*(Derivative[1][f][x]*y'[x] + f[x]*y''[x]) + Cos[y[x]]*(-(Derivative[1][q][x]*y'[x]) + q[x]*y''[x]) - y''[x]*(y'[x]*Derivative[2][f][x] + 2*Derivative[1][f][x]*y''[x] + f[x]*Derivative[3][y][x]) + y'[x]*(3*Derivative[2][f][x]*y''[x] + y'[x]*Derivative[3][f][x] + 3*Derivative[1][f][x]*Derivative[3][y][x] + f[x]*Derivative[4][y][x]) == 0,y[x],x,IncludeSingularSolutions -> True]
Not solved