28.1.134 problem 157

Internal problem ID [4440]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 2. First-Order and Simple Higher-Order Differential Equations. Page 78
Problem number : 157
Date solved : Sunday, March 30, 2025 at 03:22:24 AM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 32

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

\[ y = \frac {-2 \sin \left (x \right )^{3}+3 \sin \left (x \right ) \cos \left (x \right )+6 c_1 -3 x}{6+6 \cos \left (x \right )} \]

✓ Mathematica. Time used: 0.1 (sec). Leaf size: 39

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

\[ y(x)\to \frac {1}{24} \sec ^2\left (\frac {x}{2}\right ) (-6 x-3 \sin (x)+3 \sin (2 x)+\sin (3 x)+24 c_1) \]

✓ Sympy. Time used: 1.604 (sec). Leaf size: 27

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

\[ y{\left (x \right )} = \frac {C_{1} - \frac {x}{2} - \frac {\sin ^{3}{\left (x \right )}}{3} + \frac {\sin {\left (x \right )} \cos {\left (x \right )}}{2}}{\cos {\left (x \right )} + 1} \]