4.6.5 \(x^2 y'(x)+(1-2 x) y(x)=x^2\)

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

[_linear]

Book solution method
Linear ODE

Mathematica
cpu = 0.00676732 (sec), leaf count = 19

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

Maple
cpu = 0.008 (sec), leaf count = 16

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

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

Mathematica raw output

{{y[x] -> x^2*(1 + E^x^(-1)*C[1])}}

Maple raw input

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

Maple raw output

y(x) = x^2*(exp(1/x)*_C1+1)