4.4.10 \(x y'(x)+(3-x) y(x)+2=0\)

ODE
\[ x y'(x)+(3-x) y(x)+2=0 \] ODE Classification

[_linear]

Book solution method
Linear ODE

Mathematica
cpu = 0.00871058 (sec), leaf count = 25

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

Maple
cpu = 0.01 (sec), leaf count = 22

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

DSolve[2 + (3 - x)*y[x] + x*y'[x] == 0,y[x],x]

Mathematica raw output

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

Maple raw input

dsolve(x*diff(y(x),x)+2+(3-x)*y(x) = 0, y(x),'implicit')

Maple raw output

y(x) = (exp(x)*_C1+2*x^2+4*x+4)/x^3