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