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