Internal problem ID [3174]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 15
Problem number: 428.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Bernoulli]
Solve \begin {gather*} \boxed {y y^{\prime }-\left (\csc ^{2}\relax (x )\right )+\cot \relax (x ) y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.008 (sec). Leaf size: 32
dsolve(y(x)*diff(y(x),x) = csc(x)^2-y(x)^2*cot(x),y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {\sqrt {2 x +c_{1}}}{\sin \relax (x )} \\ y \relax (x ) = -\frac {\sqrt {2 x +c_{1}}}{\sin \relax (x )} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.476 (sec). Leaf size: 36
DSolve[y[x] y'[x]==Csc[x]^2- y[x]^2 Cot[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {2 x+c_1} \csc (x) \\ y(x)\to \sqrt {2 x+c_1} \csc (x) \\ \end{align*}