4.3.50 \(x y'(x)=x^m+y(x)\)

ODE
\[ x y'(x)=x^m+y(x) \] ODE Classification

[_linear]

Book solution method
Linear ODE

Mathematica
cpu = 0.0074508 (sec), leaf count = 19

\[\left \{\left \{y(x)\to c_1 x+\frac {x^m}{m-1}\right \}\right \}\]

Maple
cpu = 0.007 (sec), leaf count = 17

\[ \left \{ y \relax (x ) ={\frac {{x}^{m}}{m-1}}+x{\it \_C1} \right \} \] Mathematica raw input

DSolve[x*y'[x] == x^m + y[x],y[x],x]

Mathematica raw output

{{y[x] -> x^m/(-1 + m) + x*C[1]}}

Maple raw input

dsolve(x*diff(y(x),x) = x^m+y(x), y(x),'implicit')

Maple raw output

y(x) = 1/(m-1)*x^m+x*_C1