7.4.19 problem 19

Internal problem ID [91]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Section 1.5 (linear equations). Problems at page 54
Problem number : 19
Date solved : Friday, February 07, 2025 at 07:49:02 AM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 19

dsolve(diff(y(x),x)+y(x)*cot(x)=cos(x),y(x), singsol=all)
 

\[ y = -\frac {\csc \left (x \right ) \left (2 \cos \left (x \right )^{2}-4 c_1 -1\right )}{4} \]

✓ Solution by Mathematica

Time used: 0.038 (sec). Leaf size: 19

DSolve[D[y[x],x]+y[x]*Cot[x]==Cos[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\frac {1}{2} \cos (x) \cot (x)+c_1 \csc (x) \]