Internal problem ID [7775]
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]
Solve \begin {gather*} \boxed {\sin \relax (x ) y^{\prime }-y^{2} \left (\sin ^{2}\relax (x )\right )+\left (\cos \relax (x )-3 \sin \relax (x )\right ) y+4=0} \end {gather*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 28
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)
\[ y \relax (x ) = -\frac {4 \left ({\mathrm e}^{5 x} c_{1}+1\right )}{\sin \relax (x ) \left ({\mathrm e}^{5 x} c_{1}-4\right )} \]
✓ Solution by Mathematica
Time used: 0.276 (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*}