ODE
\[ x y'(x)=a y(x)+x+1 \] ODE Classification
[_linear]
Book solution method
Linear ODE
Mathematica ✓
cpu = 0.184767 (sec), leaf count = 28
\[\left \{\left \{y(x)\to -\frac {a x+a-1}{(a-1) a}+c_1 x^a\right \}\right \}\]
Maple ✓
cpu = 0.012 (sec), leaf count = 31
\[\left [y \left (x \right ) = \left (-\frac {x^{-a} \left (a x +a -1\right )}{a \left (a -1\right )}+\textit {\_C1} \right ) x^{a}\right ]\] Mathematica raw input
DSolve[x*y'[x] == 1 + x + a*y[x],y[x],x]
Mathematica raw output
{{y[x] -> -((-1 + a + a*x)/((-1 + a)*a)) + x^a*C[1]}}
Maple raw input
dsolve(x*diff(y(x),x) = 1+x+a*y(x), y(x))
Maple raw output
[y(x) = (-x^(-a)*(a*x+a-1)/a/(a-1)+_C1)*x^a]