4.5.39 \(2 x y'(x)=2 x^3-y(x)\)

ODE
\[ 2 x y'(x)=2 x^3-y(x) \] ODE Classification

[_linear]

Book solution method
Linear ODE

Mathematica
cpu = 0.00453928 (sec), leaf count = 21

\[\left \{\left \{y(x)\to \frac {c_1}{\sqrt {x}}+\frac {2 x^3}{7}\right \}\right \}\]

Maple
cpu = 0.006 (sec), leaf count = 15

\[ \left \{ y \relax (x ) ={\frac {2\,{x}^{3}}{7}}+{{\it \_C1}{\frac {1}{\sqrt {x}}}} \right \} \] Mathematica raw input

DSolve[2*x*y'[x] == 2*x^3 - y[x],y[x],x]

Mathematica raw output

{{y[x] -> (2*x^3)/7 + C[1]/Sqrt[x]}}

Maple raw input

dsolve(2*x*diff(y(x),x) = 2*x^3-y(x), y(x),'implicit')

Maple raw output

y(x) = 2/7*x^3+1/x^(1/2)*_C1