84.5.1 problem 3.1 (a)

Internal problem ID [22088]
Book : Schaums outline series. Differential Equations By Richard Bronson. 1973. McGraw-Hill Inc. ISBN 0-07-008009-7
Section : Chapter 3. Classification of first-order differential equations. Solved problems. Page 11
Problem number : 3.1 (a)
Date solved : Thursday, October 02, 2025 at 08:23:46 PM
CAS classification : [_linear]

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

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

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

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

✓ Mathematica. Time used: 0.507 (sec). Leaf size: 30

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

\begin{align*} y(x)&\to e^{-\cos (x)} \left (\int _1^xe^{\cos (K[1])+K[1]}dK[1]+c_1\right ) \end{align*}

✗ Sympy

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

Timed Out