Internal problem ID [2827]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 3
Problem number: 72.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Riccati]
Solve \begin {gather*} \boxed {y^{\prime }+4 \csc \relax (x )-\left (3-\cot \relax (x )\right ) y-\sin \relax (x ) y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 34
dsolve(diff(y(x),x)+4*csc(x) = (3-cot(x))*y(x)+y(x)^2*sin(x),y(x), singsol=all)
\[ y \relax (x ) = \frac {-4 \,{\mathrm e}^{4 x} c_{1}+{\mathrm e}^{-x}}{\sin \relax (x ) \left ({\mathrm e}^{4 x} c_{1}+{\mathrm e}^{-x}\right )} \]
✓ Solution by Mathematica
Time used: 0.281 (sec). Leaf size: 32
DSolve[y'[x]+4 Csc[x]==(3-Cot[x])y[x]+y[x]^2 Sin[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \left (-4+\frac {1}{\frac {1}{5}+c_1 e^{5 x}}\right ) \csc (x) \\ y(x)\to -4 \csc (x) \\ \end{align*}