64.5.13 problem 13

Internal problem ID [13255]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 2, section 2.3 (Linear equations). Exercises page 56
Problem number : 13
Date solved : Monday, March 31, 2025 at 07:43:43 AM
CAS classification : [_linear]

\begin{align*} \cos \left (x \right )^{2}-y \cos \left (x \right )-\left (1+\sin \left (x \right )\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 23

ode:=cos(x)^2-y(x)*cos(x)-(sin(x)+1)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\cos \left (x \right ) \sin \left (x \right )+2 c_1 +x}{2+2 \sin \left (x \right )} \]

✓ Mathematica. Time used: 0.314 (sec). Leaf size: 36

ode=(Cos[x]^2-y[x]*Cos[x])-(1+Sin[x])*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {\int _1^x\cos ^2(K[1])dK[1]+c_1}{\left (\sin \left (\frac {x}{2}\right )+\cos \left (\frac {x}{2}\right )\right )^2} \]

✓ Sympy. Time used: 0.432 (sec). Leaf size: 19

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-(sin(x) + 1)*Derivative(y(x), x) - y(x)*cos(x) + cos(x)**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {C_{1} + \frac {x}{2} + \frac {\sin {\left (2 x \right )}}{4}}{\sin {\left (x \right )} + 1} \]