22.1.131 problem 154

Internal problem ID [4437]
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 : 154
Date solved : Tuesday, September 30, 2025 at 07:32:21 AM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 18

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

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

✓ Mathematica. Time used: 0.024 (sec). Leaf size: 21

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

\begin{align*} y(x)&\to \frac {1}{2} (\sin (x)+(x+2 c_1) \sec (x)) \end{align*}

✓ Sympy. Time used: 0.569 (sec). Leaf size: 17

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

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