Internal problem ID [3336]
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]
\[ \boxed {y^{\prime }-\left (3-\cot \left (x \right )\right ) y-y^{2} \sin \left (x \right )=-4 \csc \left (x \right )} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 74
dsolve(diff(y(x),x)+4*csc(x) = (3-cot(x))*y(x)+y(x)^2*sin(x),y(x), singsol=all)
\[ y \left (x \right ) = -\frac {3 \csc \left (x \right ) \left (c_{1} \left (\operatorname {csgn}\left (\sin \left (x \right )\right )+\frac {5}{3}\right ) \left (\cos \left (x \right )+i \sin \left (x \right )\right )^{-\frac {5 i}{2}}+\left (\cos \left (x \right )+i \sin \left (x \right )\right )^{\frac {5 i}{2}} \left (\operatorname {csgn}\left (\sin \left (x \right )\right )-\frac {5}{3}\right )\right )}{2 c_{1} \left (\cos \left (x \right )+i \sin \left (x \right )\right )^{-\frac {5 i}{2}}+2 \left (\cos \left (x \right )+i \sin \left (x \right )\right )^{\frac {5 i}{2}}} \]
✓ Solution by Mathematica
Time used: 0.264 (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*}