65.4.3 problem 9.1 (iii)

Internal problem ID [13733]
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 : Tuesday, January 28, 2025 at 06:00:12 AM
CAS classification : [_linear]

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

✓ Solution by Maple

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

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

\[ z \left (y \right ) = -\frac {\cos \left (y \right )}{2}+\sec \left (y \right ) c_{1} +\frac {\sec \left (y \right )}{4} \]

✓ Solution by Mathematica

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

DSolve[D[z[y],y]==z[y]*Tan[y]+Sin[y],z[y],y,IncludeSingularSolutions -> True]
 

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