4.8.26 \(x \left (1-x^3\right ) y'(x)=2 x-\left (1-4 x^3\right ) y(x)\)

ODE
\[ x \left (1-x^3\right ) y'(x)=2 x-\left (1-4 x^3\right ) y(x) \] ODE Classification

[_linear]

Book solution method
Linear ODE

Mathematica
cpu = 0.010793 (sec), leaf count = 21

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

Maple
cpu = 0.006 (sec), leaf count = 21

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

DSolve[x*(1 - x^3)*y'[x] == 2*x - (1 - 4*x^3)*y[x],y[x],x]

Mathematica raw output

{{y[x] -> (x^2 + C[1])/(x - x^4)}}

Maple raw input

dsolve(x*(-x^3+1)*diff(y(x),x) = 2*x-(-4*x^3+1)*y(x), y(x),'implicit')

Maple raw output

y(x) = (-x^2+_C1)/(x^4-x)