88.19.10 problem 10

Internal problem ID [24138]
Book : Elementary Differential Equations. By Lee Roy Wilcox and Herbert J. Curtis. 1961 first edition. International texbook company. Scranton, Penn. USA. CAT number 61-15976
Section : Chapter 5. Special Techniques for Linear Equations. Exercises at page 139
Problem number : 10
Date solved : Thursday, October 02, 2025 at 10:00:09 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 22

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

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

✓ Mathematica. Time used: 0.019 (sec). Leaf size: 22

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

\begin{align*} y(x)&\to \left (-\frac {x}{2}+c_1\right ) \cos (x)+c_2 \sin (x) \end{align*}

✓ Sympy. Time used: 0.060 (sec). Leaf size: 15

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

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