Internal problem ID [3682]
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]
\[ \boxed {y y^{\prime }+y^{2} \cot \left (x \right )=\csc \left (x \right )^{2}} \]
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 28
dsolve(y(x)*diff(y(x),x) = csc(x)^2-y(x)^2*cot(x),y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \csc \left (x \right ) \sqrt {2 x +c_{1}} \\ y \left (x \right ) &= -\csc \left (x \right ) \sqrt {2 x +c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.489 (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*}