Internal problem ID [2771]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 1
Problem number: 16.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-\left (2 \csc \left (2 x \right )+\cot \relax (x )\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 39
dsolve(diff(y(x),x) = (2*csc(2*x)+cot(x))*y(x),y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1} \cot \relax (x ) \left (\cos \relax (x )-\cos \left (3 x \right )\right )}{\sin \left (2 x \right ) \left (\cot ^{2}\relax (x )\right )-\sin \left (2 x \right )+2 \cot \relax (x )} \]
✓ Solution by Mathematica
Time used: 0.066 (sec). Leaf size: 33
DSolve[y'[x]==(2*Csc[2*x]+Cot[x])*y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {c_1 \sin ^{\frac {3}{2}}(x) \sqrt {\sin (2 x)}}{\cos ^{\frac {3}{2}}(x)} \\ y(x)\to 0 \\ \end{align*}