Internal problem ID [7753]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 173.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, _Riccati]
Solve \begin {gather*} \boxed {x^{3} y^{\prime }-x^{6} y^{2}-\left (2 x -3\right ) x^{2} y+3=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 27
dsolve(x^3*diff(y(x),x) - x^6*y(x)^2 - (2*x-3)*x^2*y(x) + 3=0,y(x), singsol=all)
\[ y \relax (x ) = -\frac {3 \left ({\mathrm e}^{4 x} c_{1}+1\right )}{x^{3} \left ({\mathrm e}^{4 x} c_{1}-3\right )} \]
✓ Solution by Mathematica
Time used: 0.164 (sec). Leaf size: 34
DSolve[x^3*y'[x] - x^6*y[x]^2 - (2*x-3)*x^2*y[x] + 3==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {-3+\frac {1}{\frac {1}{4}+c_1 e^{4 x}}}{x^3} \\ y(x)\to -\frac {3}{x^3} \\ \end{align*}