74.1.7 problem 10

Internal problem ID [15716]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 1. Introduction to Differential Equations. Exercises 1.1, page 10
Problem number : 10
Date solved : Monday, March 31, 2025 at 01:45:54 PM
CAS classification : [NONE]

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

✗ Maple

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

\[ \text {No solution found} \]

✗ Mathematica

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

Not solved

✗ Sympy

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

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