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 = 0.146292 (sec), leaf count = 29
\[\left \{\left \{y(x)\to -\frac {3 x^2}{2}+c_1\right \},\left \{y(x)\to \frac {x^2}{2}+c_1\right \}\right \}\]
Maple ✓
cpu = 0.009 (sec), leaf count = 21
\[\left [y \left (x \right ) = \frac {x^{2}}{2}+\textit {\_C1}, y \left (x \right ) = -\frac {3 x^{2}}{2}+\textit {\_C1}\right ]\] 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))
Maple raw output
[y(x) = 1/2*x^2+_C1, y(x) = -3/2*x^2+_C1]