4.4.6 \(x y'(x)=a y(x)+x+1\)

ODE
\[ x y'(x)=a y(x)+x+1 \] ODE Classification

[_linear]

Book solution method
Linear ODE

Mathematica
cpu = 0.0149854 (sec), leaf count = 26

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

Maple
cpu = 0.01 (sec), leaf count = 31

\[ \left \{ y \relax (x ) = \left (-{\frac {{x}^{-a} \left (ax+a-1 \right ) }{a \left (a-1 \right ) }}+{\it \_C1} \right ) {x}^{a} \right \} \] Mathematica raw input

DSolve[x*y'[x] == 1 + x + a*y[x],y[x],x]

Mathematica raw output

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

Maple raw input

dsolve(x*diff(y(x),x) = 1+x+a*y(x), y(x),'implicit')

Maple raw output

y(x) = (-x^(-a)*(a*x+a-1)/a/(a-1)+_C1)*x^a