4.8.31 \(x^5 y'(x)=1-3 x^4 y(x)\)

ODE
\[ x^5 y'(x)=1-3 x^4 y(x) \] ODE Classification

[_linear]

Book solution method
Linear ODE

Mathematica
cpu = 0.00370956 (sec), leaf count = 15

\[\left \{\left \{y(x)\to \frac {c_1 x-1}{x^4}\right \}\right \}\]

Maple
cpu = 0.005 (sec), leaf count = 15

\[ \left \{ y \relax (x ) ={\frac {1}{{x}^{3}} \left (-{x}^{-1}+{\it \_C1} \right ) } \right \} \] Mathematica raw input

DSolve[x^5*y'[x] == 1 - 3*x^4*y[x],y[x],x]

Mathematica raw output

{{y[x] -> (-1 + x*C[1])/x^4}}

Maple raw input

dsolve(x^5*diff(y(x),x) = 1-3*x^4*y(x), y(x),'implicit')

Maple raw output

y(x) = (-1/x+_C1)/x^3