23.1.17 problem 13 (c)

Internal problem ID [4624]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 1. THE DIFFERENTIAL EQUATION IS OF FIRST ORDER AND OF FIRST DEGREE, page 223
Problem number : 13 (c)
Date solved : Tuesday, September 30, 2025 at 07:37:18 AM
CAS classification : [_linear]

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

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

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

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

✓ Mathematica. Time used: 0.361 (sec). Leaf size: 29

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

\begin{align*} y(x)&\to e^{-\sin (x)} \left (\int _1^xe^{2 \sin (K[1])}dK[1]+c_1\right ) \end{align*}

✓ Sympy. Time used: 2.019 (sec). Leaf size: 19

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

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