Internal problem ID [15474]
Internal file name [OUTPUT/15475_Friday_May_10_2024_03_32_48_PM_54640770/index.tex]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Chapter 2 (Higher order ODE’s). Section 18.1 Integration of differential equation in
series. Power series. Exercises page 171
Problem number: 731.
ODE order: 2.
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 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 trying differential order: 3; exact nonlinear trying 3rd order, integrating factor of the form mu(y) for some mu Trying the formal computation of integrating factors depending on any 2 of [x, y, y, y] differential order: 3; looking for linear symmetries --- Trying Lie symmetry methods, high order --- `, `-> Computing symmetries using: way = 3 `, `-> Computing symmetries using: way = 5`
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 14
Order:=6; dsolve([diff(y(x),x$3)+x*sin(y(x))=0,y(0) = 1/2*Pi, D(y)(0) = 0, (D@@2)(y)(0) = 0],y(x),type='series',x=0);
\[ y = \frac {\pi }{2}-\frac {1}{24} x^{4}+\operatorname {O}\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.055 (sec). Leaf size: 16
AsymptoticDSolveValue[{y'''[x]+x*Sin[y[x]]==0,{y[0]==Pi/2,y'[0]==0,y''[0]==0}},y[x],{x,0,5}]
\[ y(x)\to \frac {\pi }{2}-\frac {x^4}{24} \]