4.4.9 \(x y'(x)=a+b x^n+c y(x)\)

ODE
\[ x y'(x)=a+b x^n+c y(x) \] ODE Classification

[_linear]

Book solution method
Linear ODE

Mathematica
cpu = 0.0281479 (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 = 0.015 (sec), leaf count = 28

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

Maple raw output

y(x) = b/(-c+n)*x^n-1/c*a+x^c*_C1