90.20.9 problem 9

Internal problem ID [25304]
Book : Ordinary Differential Equations. By William Adkins and Mark G Davidson. Springer. NY. 2010. ISBN 978-1-4614-3617-1
Section : Chapter 5. Second Order Linear Differential Equations. Exercises at page 337
Problem number : 9
Date solved : Thursday, October 02, 2025 at 11:59:47 PM
CAS classification : [NONE]

\begin{align*} y^{\prime \prime }+2 y+t \sin \left (y\right )&=0 \end{align*}

✗ Maple

ode:=diff(diff(y(t),t),t)+2*y(t)+t*sin(y(t)) = 0; 
dsolve(ode,y(t), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=D[y[t],{t,2}]+2*y[t]+t*Sin[y[t]]==0; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(t*sin(y(t)) + 2*y(t) + Derivative(y(t), (t, 2)),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

NotImplementedError : solve: Cannot solve t*sin(y(t)) + 2*y(t) + Derivative(y(t), (t, 2))