60.1.194 problem 195

Internal problem ID [10208]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 195
Date solved : Monday, January 27, 2025 at 06:38:27 PM
CAS classification : [_Riccati]

\begin{align*} \sin \left (x \right ) y^{\prime }-y^{2} \sin \left (x \right )^{2}+\left (\cos \left (x \right )-3 \sin \left (x \right )\right ) y+4&=0 \end{align*}

✓ Solution by Maple

Time used: 0.018 (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)
 

\[ y = -\frac {4 \csc \left (x \right ) \left (1+{\mathrm e}^{5 x} c_{1} \right )}{{\mathrm e}^{5 x} c_{1} -4} \]

✓ Solution by Mathematica

Time used: 0.246 (sec). Leaf size: 32

DSolve[Sin[x]*D[y[x],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*}