81.13.9 problem 17-9

Internal problem ID [21683]
Book : The Differential Equations Problem Solver. VOL. I. M. Fogiel director. REA, NY. 1978. ISBN 78-63609
Section : Chapter 17. Reduction of Order. Page 420
Problem number : 17-9
Date solved : Thursday, October 02, 2025 at 07:59:57 PM
CAS classification : [[_2nd_order, _quadrature]]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 15

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

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

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 20

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

\begin{align*} y(x)&\to -\frac {1}{2} \cos ^2(x)+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(-cos(2*x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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