Internal problem ID [3280]
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]
\[ \boxed {y^{\prime }-\left (2 \csc \left (2 x \right )+\cot \left (x \right )\right ) y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 39
dsolve(diff(y(x),x) = (2*csc(2*x)+cot(x))*y(x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {c_{1} \cot \left (x \right ) \left (\cos \left (x \right )-\cos \left (3 x \right )\right )}{\sin \left (2 x \right ) \cot \left (x \right )^{2}-\sin \left (2 x \right )+2 \cot \left (x \right )} \]
✓ Solution by Mathematica
Time used: 0.068 (sec). Leaf size: 32
DSolve[y'[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*}