23.1.13 problem 12 (a)

Internal problem ID [4620]
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 : 12 (a)
Date solved : Tuesday, September 30, 2025 at 07:37:10 AM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 15

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

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

✓ Mathematica. Time used: 0.03 (sec). Leaf size: 18

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

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

✓ Sympy. Time used: 0.268 (sec). Leaf size: 14

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

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