4.17.40 $x^2+4x{y}^{\prime }(x)+3y^{\prime }(x{)}^2-y(x)=0$

ODE
$$x^2+4x{y}^{\prime }(x)+3y^{\prime }(x{)}^2-y(x)=0$$ ODE Classification

[[_homogeneous, `class G`]]

Book solution method
Change of variable

Mathematica ✗
cpu = 600.006 (sec), leaf count = 0 , timed out

$Aborted

Maple ✓
cpu = 0.125 (sec), leaf count = 138

$$\{1((2x^2-2\mathit{\_}\mathit{C}\mathit{1}+8y\left(x\right))\sqrt{x^2+3y\left(x\right)}-x(x^2+\mathit{\_}\mathit{C}\mathit{1}+4y\left(x\right))){(2\sqrt{x^2+3y\left(x\right)}+x)}^{-1}=0,2\frac{\sqrt{x^2+3y\left(x\right)}}{(2\sqrt{x^2+3y\left(x\right)}+x)(x^2+4y\left(x\right))}-\frac{x}{x^2+4y\left(x\right)}{(2\sqrt{x^2+3y\left(x\right)}+x)}^{-1}-\mathit{\_}\mathit{C}\mathit{1}=0,y\left(x\right)=-\frac{x^2}{3}\}$$ Mathematica raw input

DSolve[x^2 - y[x] + 4*x*y'[x] + 3*y'[x]^2 == 0,y[x],x]

Mathematica raw output

$Aborted

Maple raw input

dsolve(3*diff(y(x),x)^2+4*x*diff(y(x),x)+x^2-y(x) = 0, y(x),'implicit')

Maple raw output

y(x) = -1/3*x^2, 2/(2*(x^2+3*y(x))^(1/2)+x)/(x^2+4*y(x))*(x^2+3*y(x))^(1/2)-1/(2
*(x^2+3*y(x))^(1/2)+x)/(x^2+4*y(x))*x-_C1 = 0, ((2*x^2-2*_C1+8*y(x))*(x^2+3*y(x)
)^(1/2)-x*(x^2+_C1+4*y(x)))/(2*(x^2+3*y(x))^(1/2)+x) = 0