4.7.37 $2(1-x)x{y}^{\prime }(x)+(1-2x)y(x)+x=0$

ODE
$$2(1-x)x{y}^{\prime }(x)+(1-2x)y(x)+x=0$$ ODE Classification

[_linear]

Book solution method
Linear ODE

Mathematica ✓
cpu = 0.035545 (sec), leaf count = 66

$$\left\{\{y(x)\to \frac{2c_1\sqrt{-(x-1)x}-x^2+x-\sqrt{x-1}\sqrt{x}\log (\sqrt{x-1}+\sqrt{x})}{2x-2x^2}\}\right\}$$

Maple ✓
cpu = 0.017 (sec), leaf count = 37

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

DSolve[x + (1 - 2*x)*y[x] + 2*(1 - x)*x*y'[x] == 0,y[x],x]

Mathematica raw output

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

Maple raw input

dsolve(2*x*(1-x)*diff(y(x),x)+x+(1-2*x)*y(x) = 0, y(x),'implicit')

Maple raw output

y(x) = 1/4*(2*(x*(-1+x))^(1/2)+ln(-1/2+x+(x*(-1+x))^(1/2))+4*_C1)/(x*(-1+x))^(1/
2)