20.3.25 problem Problem 32

Internal problem ID [3634]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 1, First-Order Differential Equations. Section 1.6, First-Order Linear Differential Equations. page 59
Problem number : Problem 32
Date solved : Monday, January 27, 2025 at 07:48:01 AM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 16

dsolve(diff(y(x),x)+y(x)*cot(x)=2*cos(x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.037 (sec). Leaf size: 20

DSolve[D[y[x],x]+y[x]*Cot[x]==2*Cos[x],y[x],x,IncludeSingularSolutions -> True]
 

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