Internal problem ID [3205]
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]]
Solve \begin {gather*} \boxed {\left (y-\cot \relax (x ) \csc \relax (x )\right ) y^{\prime }+\csc \relax (x ) \left (1+\cos \relax (x ) y\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 70
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 \relax (x ) = \frac {\sin \relax (x ) \sqrt {\frac {c_{1} \left (\sin ^{2}\relax (x )\right )+1}{\sin \relax (x )^{2}}}-\cos \relax (x )}{\cos ^{2}\relax (x )-1} \\ y \relax (x ) = -\frac {\sin \relax (x ) \sqrt {\frac {c_{1} \left (\sin ^{2}\relax (x )\right )+1}{\sin \relax (x )^{2}}}+\cos \relax (x )}{\cos ^{2}\relax (x )-1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 1.49 (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*}