4.8.34 \(x^n y'(x)=a+b x^{n-1} y(x)\)

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

\[ \left \{ y \relax (x ) =-{\frac {a{x}^{1-n}}{n+b-1}}+{x}^{b}{\it \_C1} \right \} \] 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