81.6.18 problem 7-17

Internal problem ID [21564]
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 : 7-17
Date solved : Thursday, October 02, 2025 at 07:49:33 PM
CAS classification : [[_linear, `class A`]]

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

With initial conditions

\begin{align*} y \left (\pi \right )&=1 \\ \end{align*}

✓ Maple. Time used: 0.016 (sec). Leaf size: 21

ode:=diff(y(x),x)+y(x) = sin(x); 
ic:=[y(Pi) = 1]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.029 (sec). Leaf size: 23

ode=D[y[x],x]+y[x]==Sin[x]; 
ic={y[Pi]==1}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.081 (sec). Leaf size: 20

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(y(x) - sin(x) + Derivative(y(x), x),0) 
ics = {y(pi): 1} 
dsolve(ode,func=y(x),ics=ics)
 

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