24.1.4 problem 1(d)

Internal problem ID [4193]
Book : Elementary Differential equations, Chaundy, 1969
Section : Exercises 3, page 60
Problem number : 1(d)
Date solved : Monday, January 27, 2025 at 08:41:43 AM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 19

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

\[ y \left (x \right ) = \csc \left (x \right ) \left (-\sin \left (x \right )+\ln \left (\sec \left (x \right )+\tan \left (x \right )\right )+c_{1} \right ) \]

✓ Solution by Mathematica

Time used: 0.040 (sec). Leaf size: 18

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

\[ y(x)\to \csc (x) \text {arctanh}(\sin (x))+c_1 \csc (x)-1 \]