1.22 problem 21

Internal problem ID [2776]

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]

Solve \begin {gather*} \boxed {y^{\prime }-2 \left (\cot ^{2}\relax (x )\right ) \cos \left (2 x \right )+2 y \csc \left (2 x \right )=0} \end {gather*}

Solution by Maple

Time used: 0.016 (sec). Leaf size: 32

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

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

Solution by Mathematica

Time used: 0.106 (sec). Leaf size: 21

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

\begin{align*} y(x)\to \cot (x) (\cos (2 x)+2 \log (\sin (x))-1+c_1) \\ \end{align*}