Internal problem ID [3713]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 16
Problem number: 459.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_Abel, `2nd type`, `class A`]]
\[ \boxed {\left (y-\cot \left (x \right ) \csc \left (x \right )\right ) y^{\prime }+\csc \left (x \right ) \left (1+y \cos \left (x \right )\right ) y=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 51
dsolve((y(x)-cot(x)*csc(x))*diff(y(x),x)+csc(x)*(1+y(x)*cos(x))*y(x) = 0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = -\frac {-\csc \left (x \right ) \cot \left (x \right ) \sin \left (x \right )+\sqrt {c_{1} +\cot \left (x \right )^{2}}}{\sin \left (x \right )} y \left (x \right ) = \frac {\csc \left (x \right ) \cot \left (x \right ) \sin \left (x \right )+\sqrt {c_{1} +\cot \left (x \right )^{2}}}{\sin \left (x \right )} \end{align*}
✓ Solution by Mathematica
Time used: 1.639 (sec). Leaf size: 85
DSolve[(y[x]-Cot[x] Csc[x])y'[x]+Csc[x](1+y[x] Cos[x])y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \cot (x) \csc (x)-\frac {i \csc ^2(x) \sqrt {(-1+c_1) \cos (2 x)-1-c_1}}{\sqrt {2}} y(x)\to \cot (x) \csc (x)+\frac {i \csc ^2(x) \sqrt {(-1+c_1) \cos (2 x)-1-c_1}}{\sqrt {2}} \end{align*}