29.1.17 problem 16

Internal problem ID [4624]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 1
Problem number : 16
Date solved : Monday, January 27, 2025 at 09:26:37 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 10

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

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

✓ Solution by Mathematica

Time used: 0.057 (sec). Leaf size: 32

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

\begin{align*} y(x)\to c_1 \sqrt {\sin (2 x)} e^{-\frac {3}{2} \text {arctanh}(\cos (2 x))} \\ y(x)\to 0 \\ \end{align*}