67.4.18 problem 5.2 (h)

Internal problem ID [16387]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 5. LINEAR FIRST ORDER EQUATIONS. Additional exercises. page 103
Problem number : 5.2 (h)
Date solved : Thursday, October 02, 2025 at 01:27:24 PM
CAS classification : [_linear]

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

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

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

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

✓ Mathematica. Time used: 0.028 (sec). Leaf size: 12

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

\begin{align*} y(x)&\to (x+c_1) \cos (x) \end{align*}

✓ Sympy. Time used: 0.282 (sec). Leaf size: 8

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)
 

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