23.1.425 problem 415

Internal problem ID [5032]
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 : 415
Date solved : Tuesday, September 30, 2025 at 11:28:02 AM
CAS classification : [_separable]

\begin{align*} \left (1-\sin \left (x \right )\right ) y^{\prime }+y \cos \left (x \right )&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 10

ode:=(1-sin(x))*diff(y(x),x)+y(x)*cos(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 \left (-1+\sin \left (x \right )\right ) \]

✓ Mathematica. Time used: 0.18 (sec). Leaf size: 58

ode=(1-Sin[x])*D[y[x],x]+y[x]*Cos[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 \left (\frac {K[1]}{2}\right )+\sin \left (\frac {K[1]}{2}\right )}{\cos \left (\frac {K[1]}{2}\right )-\sin \left (\frac {K[1]}{2}\right )}dK[1]\right )\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.184 (sec). Leaf size: 8

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((1 - sin(x))*Derivative(y(x), x) + y(x)*cos(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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