Internal problem ID [3098]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 12
Problem number: 350.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, _Riccati]
Solve \begin {gather*} \boxed {y^{\prime } x^{3}+3+\left (-2 x +3\right ) x^{2} y-x^{6} y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 27
dsolve(x^3*diff(y(x),x)+3+(3-2*x)*x^2*y(x)-x^6*y(x)^2 = 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: 0.17 (sec). Leaf size: 34
DSolve[x^3 y'[x]+3+(3-2 x)x^2 y[x]-x^6 y[x]^2==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*}