67.1.20 problem 2.3 (j)

Internal problem ID [16285]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 2. Integration and differential equations. Additional exercises. page 32
Problem number : 2.3 (j)
Date solved : Thursday, October 02, 2025 at 10:45:21 AM
CAS classification : [[_2nd_order, _quadrature]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 15

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

\[ y = -\frac {\sin \left (2 x \right )}{4}+c_1 x +c_2 \]

✓ Mathematica. Time used: 0.007 (sec). Leaf size: 32

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

\begin{align*} y(x)&\to \int _1^x\int _1^{K[2]}\sin (2 K[1])dK[1]dK[2]+c_2 x+c_1 \end{align*}

✓ Sympy. Time used: 0.032 (sec). Leaf size: 14

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

\[ y{\left (x \right )} = C_{1} + C_{2} x - \frac {\sin {\left (2 x \right )}}{4} \]