81.6.11 problem 7-11

Internal problem ID [21557]
Book : The Differential Equations Problem Solver. VOL. I. M. Fogiel director. REA, NY. 1978. ISBN 78-63609
Section : Chapter 7. Linear Differential Equations. Page 101.
Problem number : 7-11
Date solved : Thursday, October 02, 2025 at 07:48:08 PM
CAS classification : [[_linear, `class A`]]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 19

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

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

✓ Mathematica. Time used: 0.025 (sec). Leaf size: 25

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

\begin{align*} y(x)&\to \frac {1}{2} \left (\sin (x)-\cos (x)+2 c_1 e^{-x}\right ) \end{align*}

✓ Sympy. Time used: 0.076 (sec). Leaf size: 17

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

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