4.5.45 \((1-2 x) y'(x)=2 (-3 y(x)+16 x+8)\)

ODE
\[ (1-2 x) y'(x)=2 (-3 y(x)+16 x+8) \] ODE Classification

[_linear]

Book solution method
Linear ODE

Mathematica
cpu = 0.0125542 (sec), leaf count = 22

\[\left \{\left \{y(x)\to c_1 (2 x-1)^3+8 x+\frac {4}{3}\right \}\right \}\]

Maple
cpu = 0.013 (sec), leaf count = 18

\[ \left \{ y \relax (x ) ={\frac {4}{3}}+8\,x+ \left (-1+2\,x \right ) ^{3}{\it \_C1} \right \} \] Mathematica raw input

DSolve[(1 - 2*x)*y'[x] == 2*(8 + 16*x - 3*y[x]),y[x],x]

Mathematica raw output

{{y[x] -> 4/3 + 8*x + (-1 + 2*x)^3*C[1]}}

Maple raw input

dsolve((1-2*x)*diff(y(x),x) = 16+32*x-6*y(x), y(x),'implicit')

Maple raw output

y(x) = 4/3+8*x+(-1+2*x)^3*_C1