4.8.34 xny(x)=a+bxn1y(x)

ODE
xny(x)=a+bxn1y(x) ODE Classification

[_linear]

Book solution method
Linear ODE

Mathematica
cpu = 0.0169469 (sec), leaf count = 28

{{y(x)c1xbax1nb+n1}}

Maple
cpu = 0.011 (sec), leaf count = 26

{y(x)=ax1nn+b1+xb_C1} 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