29.1.16 problem 15

Internal problem ID [4623]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 1
Problem number : 15
Date solved : Monday, January 27, 2025 at 09:26:35 AM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 14

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

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

✓ Solution by Mathematica

Time used: 0.038 (sec). Leaf size: 19

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

\[ y(x)\to \frac {1}{2} \left (x^2+2 c_1\right ) \csc (x) \]