29.1.20 problem 19

Internal problem ID [4627]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 1
Problem number : 19
Date solved : Monday, January 27, 2025 at 09:26:45 AM
CAS classification : [_linear]

\begin{align*} y^{\prime }+\csc \left (x \right )+2 y \cot \left (x \right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 13

dsolve(diff(y(x),x)+csc(x)+2*y(x)*cot(x) = 0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.036 (sec). Leaf size: 15

DSolve[D[y[x],x]+Csc[x]+2*y[x]*Cot[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \csc ^2(x) (\cos (x)+c_1) \]