4.3.46 \(x y'(x)+y(x)+x=0\)

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

[_linear]

Book solution method
Linear ODE

Mathematica
cpu = 0.00348525 (sec), leaf count = 17

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

Maple
cpu = 0.006 (sec), leaf count = 13

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

DSolve[x + y[x] + x*y'[x] == 0,y[x],x]

Mathematica raw output

{{y[x] -> -x/2 + C[1]/x}}

Maple raw input

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

Maple raw output

y(x) = -1/2*x+1/x*_C1