4.7.35 \((1-2 x) x y'(x)+(1-4 x) y(x)+1=0\)

ODE
\[ (1-2 x) x y'(x)+(1-4 x) y(x)+1=0 \] ODE Classification

[_linear]

Book solution method
Linear ODE

Mathematica
cpu = 0.0089752 (sec), leaf count = 22

\[\left \{\left \{y(x)\to -\frac {x-c_1}{x-2 x^2}\right \}\right \}\]

Maple
cpu = 0.009 (sec), leaf count = 18

\[ \left \{ y \relax (x ) ={\frac {x+{\it \_C1}}{x \left (-1+2\,x \right ) }} \right \} \] Mathematica raw input

DSolve[1 + (1 - 4*x)*y[x] + (1 - 2*x)*x*y'[x] == 0,y[x],x]

Mathematica raw output

{{y[x] -> -((x - C[1])/(x - 2*x^2))}}

Maple raw input

dsolve(x*(1-2*x)*diff(y(x),x)+1+(1-4*x)*y(x) = 0, y(x),'implicit')

Maple raw output

y(x) = (x+_C1)/x/(-1+2*x)