4.12.6 \(-3 x^2+2 (x+1) y(x) y'(x)+y(x)^2+2 x=0\)

ODE
\[ -3 x^2+2 (x+1) y(x) y'(x)+y(x)^2+2 x=0 \] ODE Classification

[_exact, _rational, _Bernoulli]

Book solution method
Exact equation

Mathematica
cpu = 0.0136598 (sec), leaf count = 56

\[\left \{\left \{y(x)\to -\frac {\sqrt {c_1+x^3-x^2}}{\sqrt {x+1}}\right \},\left \{y(x)\to \frac {\sqrt {c_1+x^3-x^2}}{\sqrt {x+1}}\right \}\right \}\]

Maple
cpu = 0.009 (sec), leaf count = 26

\[ \left \{ \left (y \relax (x ) \right ) ^{2}+{\frac {-{x}^{3}+{x}^{2}-{\it \_C1}}{1+x}}=0 \right \} \] Mathematica raw input

DSolve[2*x - 3*x^2 + y[x]^2 + 2*(1 + x)*y[x]*y'[x] == 0,y[x],x]

Mathematica raw output

{{y[x] -> -(Sqrt[-x^2 + x^3 + C[1]]/Sqrt[1 + x])}, {y[x] -> Sqrt[-x^2 + x^3 + C[
1]]/Sqrt[1 + x]}}

Maple raw input

dsolve(2*(1+x)*y(x)*diff(y(x),x)+2*x-3*x^2+y(x)^2 = 0, y(x),'implicit')

Maple raw output

y(x)^2+(-x^3+x^2-_C1)/(1+x) = 0