ODE
\[ x^n y'(x)=a+b x^{n-1} y(x) \] ODE Classification
[_linear]
Book solution method
Linear ODE
Mathematica ✓
cpu = 0.0169469 (sec), leaf count = 28
\[\left \{\left \{y(x)\to c_1 x^b-\frac {a x^{1-n}}{b+n-1}\right \}\right \}\]
Maple ✓
cpu = 0.011 (sec), leaf count = 26
\[ \left \{ y \left ( x \right ) =-{\frac {a{x}^{1-n}}{n+b-1}}+{x}^{b}{\it \_C1} \right \} \] 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),'implicit')
Maple raw output
y(x) = -a*x^(1-n)/(n+b-1)+x^b*_C1