29.1.14 problem 13

Internal problem ID [4621]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 1
Problem number : 13
Date solved : Monday, January 27, 2025 at 09:26:31 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 8

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

\[ y \left (x \right ) = c_{1} \sin \left (x \right ) \]

✓ Solution by Mathematica

Time used: 0.034 (sec). Leaf size: 15

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

\begin{align*} y(x)\to c_1 \sin (x) \\ y(x)\to 0 \\ \end{align*}