29.1.22 problem 21

Internal problem ID [4629]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 1
Problem number : 21
Date solved : Monday, January 27, 2025 at 09:27:05 AM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 20

dsolve(diff(y(x),x) = 2*cot(x)^2*cos(2*x)-2*y(x)*csc(2*x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.074 (sec). Leaf size: 21

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

\[ y(x)\to \cot (x) (\cos (2 x)+2 \log (\sin (x))-1+c_1) \]