4.42.19 $3x^2{y}^{″}(x{)}^2+4y^{\prime }(x{)}^2-2(3x{y}^{\prime }(x)+y(x))y^{″}(x)=0$

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

[[_2nd_order, _with_linear_symmetries]]

Book solution method
TO DO

Mathematica ✓
cpu = 0.00891545 (sec), leaf count = 24

$$\left\{\{y(x)\to \frac{c_1^2{x}^2}{c_2}+c_{1}x+c_2\}\right\}$$

Maple ✓
cpu = 0.241 (sec), leaf count = 41

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

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

Mathematica raw output

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

Maple raw input

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

Maple raw output

1/2*3^(1/2)*ln(y(x)/x)-ln(x)-_C1 = 0, y(x) = _C1^2/_C2*x^2+_C1*x+_C2