81.3.2 problem 2

Internal problem ID [18620]
Book : A short course on differential equations. By Donald Francis Campbell. Maxmillan company. London. 1907
Section : Chapter III. Ordinary differential equations of the first order and first degree. Exercises at page 33
Problem number : 2
Date solved : Tuesday, January 28, 2025 at 12:04:22 PM
CAS classification : [_linear]

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

✓ Solution by Maple

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

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

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

✓ Solution by Mathematica

Time used: 0.036 (sec). Leaf size: 16

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

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