ODE
\[ x y'(x)=a+b x^n+c y(x) \] ODE Classification
[_linear]
Book solution method
Linear ODE
Mathematica ✓
cpu = 0.202495 (sec), leaf count = 31
\[\left \{\left \{y(x)\to -\frac {a}{c}-\frac {b x^n}{c-n}+c_1 x^c\right \}\right \}\]
Maple ✓
cpu = 0.019 (sec), leaf count = 28
\[\left [y \left (x \right ) = -\frac {a}{c}+\frac {x^{n} b}{-c +n}+x^{c} \textit {\_C1}\right ]\] Mathematica raw input
DSolve[x*y'[x] == a + b*x^n + c*y[x],y[x],x]
Mathematica raw output
{{y[x] -> -(a/c) - (b*x^n)/(c - n) + x^c*C[1]}}
Maple raw input
dsolve(x*diff(y(x),x) = a+b*x^n+c*y(x), y(x))
Maple raw output
[y(x) = -1/c*a+1/(-c+n)*x^n*b+x^c*_C1]