64.5.13 problem 13

Internal problem ID [13326]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 2, section 2.3 (Linear equations). Exercises page 56
Problem number : 13
Date solved : Tuesday, January 28, 2025 at 05:22:18 AM
CAS classification : [_linear]

\begin{align*} \cos \left (x \right )^{2}-y \cos \left (x \right )-\left (1+\sin \left (x \right )\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 23

dsolve((cos(x)^2-y(x)*cos(x))-(1+sin(x))*diff(y(x),x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.314 (sec). Leaf size: 36

DSolve[(Cos[x]^2-y[x]*Cos[x])-(1+Sin[x])*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {\int _1^x\cos ^2(K[1])dK[1]+c_1}{\left (\sin \left (\frac {x}{2}\right )+\cos \left (\frac {x}{2}\right )\right )^2} \]