ODE
\[ x^n y'(x)=a+b x^{n-1} y(x) \] ODE Classification
[_linear]
Book solution method
Linear ODE
Mathematica ✓
cpu = 0.211605 (sec), leaf count = 28
\[\left \{\left \{y(x)\to -\frac {a x^{1-n}}{b+n-1}+c_1 x^b\right \}\right \}\]
Maple ✓
cpu = 0.011 (sec), leaf count = 26
\[\left [y \left (x \right ) = -\frac {x^{1-n} a}{n +b -1}+x^{b} \textit {\_C1}\right ]\] Mathematica raw input
DSolve[x^n*y'[x] == a + b*x^(-1 + n)*y[x],y[x],x]
Mathematica raw output
{{y[x] -> -((a*x^(1 - n))/(-1 + b + n)) + x^b*C[1]}}
Maple raw input
dsolve(x^n*diff(y(x),x) = a+b*x^(n-1)*y(x), y(x))
Maple raw output
[y(x) = -1/(n+b-1)*x^(1-n)*a+x^b*_C1]