4.42.20 $(2-9x)x^2{y}^{″}(x{)}^2+6y(x)y^{″}(x)-6(1-6x)x{y}^{\prime }(x)y^{″}(x)=36x{y}^{\prime }(x{)}^2$

ODE
$$(2-9x)x^2{y}^{″}(x{)}^2+6y(x)y^{″}(x)-6(1-6x)x{y}^{\prime }(x)y^{″}(x)=36x{y}^{\prime }(x{)}^2$$ ODE Classification

[[_2nd_order, _with_linear_symmetries]]

Book solution method
TO DO

Mathematica ✓
cpu = 0.0301113 (sec), leaf count = 24

$$\left\{\{y(x)\to \frac{c_1^2{x}^3}{c_2}+c_{1}x+c_2\}\right\}$$

Maple ✓
cpu = 0.516 (sec), leaf count = 311

$$\{\mathit{\_}\mathit{C}\mathit{1}x{((9x-1)\sqrt{9}+9\sqrt{9x^2-2x})}^{\frac{2\sqrt{9}}{9}}{((9x-1)\sqrt{9}+9\sqrt{x(9x-2)})}^{\frac{5\sqrt{9}}{18}}\sqrt{4x-1}{\mathrm{e}}^{-2\sqrt{9x^2-2x}+\frac{\sqrt{16}}{2}\sqrt{x(9x-2)}}\frac{1}{\sqrt{1(\frac{\sqrt{16}}{2}(-\frac{1}{2}+\frac{5x}{2})\frac{1}{\sqrt{x(9x-2)}}+1)\frac{1}{\sqrt{\frac{-16x^2+8x-1}{x(9x-2)}}}}}+y\left(x\right)=0,\frac{\mathit{\_}\mathit{C}\mathit{1}\sqrt{5}\sqrt{4}x}{4}{((9x-1)\sqrt{9}+9\sqrt{9x^2-2x})}^{-\frac{2\sqrt{9}}{9}}{((9x-1)\sqrt{9}+9\sqrt{9x^2-2x})}^{-\frac{5\sqrt{9}}{18}}\sqrt{1(\frac{4}{5}+\sqrt{16}(x-\frac{1}{5})\frac{1}{\sqrt{9x^2-2x}})\frac{1}{\sqrt{-\frac{{(4x-1)}^2}{9x^2-2x}}}}\sqrt{4x-1}{\mathrm{e}}^{-\frac{-4+\sqrt{16}}{2}\sqrt{9x^2-2x}}+y\left(x\right)=0,y\left(x\right)=\mathit{\_}\mathit{C}\mathit{2}{x}^3+\mathit{\_}\mathit{C}\mathit{1}x+\frac{{\mathit{\_}\mathit{C}\mathit{1}}^2}{\mathit{\_}\mathit{C}\mathit{2}}\}$$ Mathematica raw input

DSolve[6*y[x]*y''[x] - 6*(1 - 6*x)*x*y'[x]*y''[x] + (2 - 9*x)*x^2*y''[x]^2 == 36*x*y'[x]^2,y[x],x]

Mathematica raw output

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

Maple raw input

dsolve(x^2*(2-9*x)*diff(diff(y(x),x),x)^2-6*x*(1-6*x)*diff(y(x),x)*diff(diff(y(x),x),x)+6*y(x)*diff(diff(y(x),x),x) = 36*x*diff(y(x),x)^2, y(x),'implicit')

Maple raw output

1/4*_C1*((9*x-1)*9^(1/2)+9*(9*x^2-2*x)^(1/2))^(-2/9*9^(1/2))*((9*x-1)*9^(1/2)+9*
(9*x^2-2*x)^(1/2))^(-5/18*9^(1/2))*5^(1/2)*4^(1/2)*(1/(-(4*x-1)^2/(9*x^2-2*x))^(
1/2)*(4/5+16^(1/2)*(x-1/5)/(9*x^2-2*x)^(1/2)))^(1/2)*x*(4*x-1)^(1/2)*exp(-1/2*(9
*x^2-2*x)^(1/2)*(-4+16^(1/2)))+y(x) = 0, _C1*((9*x-1)*9^(1/2)+9*(9*x^2-2*x)^(1/2
))^(2/9*9^(1/2))*((9*x-1)*9^(1/2)+9*(x*(9*x-2))^(1/2))^(5/18*9^(1/2))/((1/2*(-1/
2+5/2*x)*16^(1/2)/(x*(9*x-2))^(1/2)+1)/((-16*x^2+8*x-1)/x/(9*x-2))^(1/2))^(1/2)*
x*(4*x-1)^(1/2)*exp(-2*(9*x^2-2*x)^(1/2)+1/2*16^(1/2)*(x*(9*x-2))^(1/2))+y(x) = 
0, y(x) = _C2*x^3+_C1*x+_C1^2/_C2