65.4.3 problem 9.1 (iii)

Internal problem ID [13662]
Book : AN INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS by JAMES C. ROBINSON. Cambridge University Press 2004
Section : Chapter 9, First order linear equations and the integrating factor. Exercises page 86
Problem number : 9.1 (iii)
Date solved : Monday, March 31, 2025 at 08:07:00 AM
CAS classification : [_linear]

\begin{align*} z^{\prime }&=z \tan \left (y \right )+\sin \left (y \right ) \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 17

ode:=diff(z(y),y) = z(y)*tan(y)+sin(y); 
dsolve(ode,z(y), singsol=all);
 

\[ z = -\frac {\cos \left (y \right )}{2}+c_1 \sec \left (y \right )+\frac {\sec \left (y \right )}{4} \]

✓ Mathematica. Time used: 0.039 (sec). Leaf size: 17

ode=D[z[y],y]==z[y]*Tan[y]+Sin[y]; 
ic={}; 
DSolve[{ode,ic},z[y],y,IncludeSingularSolutions->True]
 

\[ z(y)\to -\frac {\cos (y)}{2}+c_1 \sec (y) \]

✓ Sympy. Time used: 0.816 (sec). Leaf size: 12

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

\[ z{\left (y \right )} = \frac {C_{1}}{\cos {\left (y \right )}} - \frac {\cos {\left (y \right )}}{2} \]