Internal problem ID [3285]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 1
Problem number: 21.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {y^{\prime }+2 y \csc \left (2 x \right )=2 \cot \left (x \right )^{2} \cos \left (2 x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 27
dsolve(diff(y(x),x) = 2*cot(x)^2*cos(2*x)-2*y(x)*csc(2*x),y(x), singsol=all)
\[ y \left (x \right ) = \left (2 \ln \left (\sin \left (x \right )\right )+2 \cos \left (x \right )^{2}+c_{1} \right ) \left (\csc \left (2 x \right )+\cot \left (2 x \right )\right ) \]
✓ Solution by Mathematica
Time used: 0.088 (sec). Leaf size: 21
DSolve[y'[x]==2*(Cot[x]^2*Cos[2*x]-y[x]*Csc[2*x]),y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \cot (x) (\cos (2 x)+2 \log (\sin (x))-1+c_1) \]