23.8 problem 731

Internal problem ID [15475]

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.

CAS Maple gives this as type [NONE]

✓ 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}]
                                                                                    
                                                                                    
 

\[ y(x)\to \frac {\pi }{2}-\frac {x^4}{24} \]