67.1.27 problem 2.4 (e)

Internal problem ID [16292]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 2. Integration and differential equations. Additional exercises. page 32
Problem number : 2.4 (e)
Date solved : Thursday, October 02, 2025 at 10:45:25 AM
CAS classification : [_quadrature]

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

With initial conditions

\begin{align*} y \left (0\right )&=3 \\ \end{align*}

✓ Maple. Time used: 0.023 (sec). Leaf size: 11

ode:=diff(y(x),x)*cos(x)-sin(x) = 0; 
ic:=[y(0) = 3]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = -\ln \left (\cos \left (x \right )\right )+3 \]

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 12

ode=Cos[x]*D[y[x],x]-Sin[x]==0; 
ic={y[0]==3}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to 3-\log (\cos (x)) \end{align*}

✓ Sympy. Time used: 0.084 (sec). Leaf size: 8

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-sin(x) + cos(x)*Derivative(y(x), x),0) 
ics = {y(0): 3} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = 3 - \log {\left (\cos {\left (x \right )} \right )} \]