4.16.44 \(-3 x^2+2 x y'(x)+y'(x)^2=0\)

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

[_quadrature]

Book solution method
Missing Variables ODE, Dependent variable missing, Solve for \(y'\)

Mathematica
cpu = 0.00271602 (sec), leaf count = 29

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

Maple
cpu = 0.006 (sec), leaf count = 21

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

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

Mathematica raw output

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

Maple raw input

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

Maple raw output

y(x) = 1/2*x^2+_C1, y(x) = -3/2*x^2+_C1