ODE
\[ x^6 \left (-y(x)^2\right )+x^3 y'(x)+(3-2 x) x^2 y(x)+3=0 \] ODE Classification
[_rational, _Riccati]
Book solution method
Riccati ODE, Generalized ODE
Mathematica ✓
cpu = 0.241765 (sec), leaf count = 25
\[\left \{\left \{y(x)\to \frac {-3+\frac {1}{\frac {1}{4}+c_1 e^{4 x}}}{x^3}\right \}\right \}\]
Maple ✓
cpu = 0.114 (sec), leaf count = 27
\[\left [y \left (x \right ) = -\frac {3 \left ({\mathrm e}^{4 x} \textit {\_C1} +1\right )}{x^{3} \left ({\mathrm e}^{4 x} \textit {\_C1} -3\right )}\right ]\] Mathematica raw input
DSolve[3 + (3 - 2*x)*x^2*y[x] - x^6*y[x]^2 + x^3*y'[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (-3 + (1/4 + E^(4*x)*C[1])^(-1))/x^3}}
Maple raw input
dsolve(x^3*diff(y(x),x)+3+(3-2*x)*x^2*y(x)-x^6*y(x)^2 = 0, y(x))
Maple raw output
[y(x) = -3*(exp(x)^4*_C1+1)/x^3/(exp(x)^4*_C1-3)]