78.1.5 problem 1.e

Internal problem ID [20931]
Book : A FIRST COURSE IN DIFFERENTIAL EQUATIONS FOR SCIENTISTS AND ENGINEERS. By Russell Herman. University of North Carolina Wilmington. LibreText. compiled on 06/09/2025
Section : Chapter 1, First order ODEs. Problems section 1.5
Problem number : 1.e
Date solved : Thursday, October 02, 2025 at 06:49:26 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 13

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

\[ y = -1+{\mathrm e}^{-\cos \left (x \right )} c_1 \]

✓ Mathematica. Time used: 0.035 (sec). Leaf size: 21

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

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

✓ Sympy. Time used: 0.160 (sec). Leaf size: 10

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

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