4.6.9 \(x^2 y'(x)+2 (1-x) x y(x)=e^x \left (2 e^x-1\right )\)

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

[_linear]

Book solution method
Linear ODE

Mathematica
cpu = 0.0136623 (sec), leaf count = 24

\[\left \{\left \{y(x)\to \frac {e^x \left (e^x \left (c_1+2 x\right )+1\right )}{x^2}\right \}\right \}\]

Maple
cpu = 0.009 (sec), leaf count = 21

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

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

Mathematica raw output

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

Maple raw input

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

Maple raw output

y(x) = (exp(-x)+2*x+_C1)/x^2*exp(2*x)