29.1.19 problem 18

Internal problem ID [4626]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 1
Problem number : 18
Date solved : Monday, January 27, 2025 at 09:26:43 AM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 11

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

\[ y \left (x \right ) = \left ({\mathrm e}^{x}+c_{1} \right ) \sin \left (x \right ) \]

✓ Solution by Mathematica

Time used: 0.079 (sec). Leaf size: 14

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

\[ y(x)\to \left (e^x+c_1\right ) \sin (x) \]