23.1.426 problem 416

Internal problem ID [5033]
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 : 416
Date solved : Tuesday, September 30, 2025 at 11:28:05 AM
CAS classification : [_separable]

\begin{align*} \left (\cos \left (x \right )-\sin \left (x \right )\right ) y^{\prime }+y \left (\cos \left (x \right )+\sin \left (x \right )\right )&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 13

ode:=(cos(x)-sin(x))*diff(y(x),x)+y(x)*(cos(x)+sin(x)) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 \left (\cos \left (x \right )-\sin \left (x \right )\right ) \]

✓ Mathematica. Time used: 0.074 (sec). Leaf size: 42

ode=(Cos[x]-Sin[x])*D[y[x],x]+y[x]*(Cos[x]+Sin[x])==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to c_1 \exp \left (\int _1^x-\frac {\cos (K[1])+\sin (K[1])}{\cos (K[1])-\sin (K[1])}dK[1]\right )\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.446 (sec). Leaf size: 17

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

\[ y{\left (x \right )} = \frac {C_{1}}{\sqrt {\tan ^{2}{\left (x + \frac {\pi }{4} \right )} + 1}} \]