Internal problem ID [8531]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 195.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Riccati]
\[ \boxed {y^{\prime } \sin \left (x \right )-y^{2} \sin \left (x \right )^{2}+\left (\cos \left (x \right )-3 \sin \left (x \right )\right ) y=-4} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 26
dsolve(sin(x)*diff(y(x),x) - y(x)^2*sin(x)^2 + (cos(x) - 3*sin(x))*y(x) + 4=0,y(x), singsol=all)
\[ y \left (x \right ) = -\frac {4 \csc \left (x \right ) \left (c_{1} {\mathrm e}^{5 x}+1\right )}{c_{1} {\mathrm e}^{5 x}-4} \]
✓ Solution by Mathematica
Time used: 0.267 (sec). Leaf size: 32
DSolve[Sin[x]*y'[x] - y[x]^2*Sin[x]^2 + (Cos[x] - 3*Sin[x])*y[x] + 4==0,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*}