4.3.48 \(x y'(x)=x^3-y(x)\)

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

[_linear]

Book solution method
Linear ODE

Mathematica
cpu = 0.00347406 (sec), leaf count = 19

\[\left \{\left \{y(x)\to \frac {c_1}{x}+\frac {x^3}{4}\right \}\right \}\]

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

\[ \left \{ y \relax (x ) ={\frac {1}{x} \left ({\frac {{x}^{4}}{4}}+{\it \_C1} \right ) } \right \} \] Mathematica raw input

DSolve[x*y'[x] == x^3 - y[x],y[x],x]

Mathematica raw output

{{y[x] -> x^3/4 + C[1]/x}}

Maple raw input

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

Maple raw output

y(x) = (1/4*x^4+_C1)/x