4.5.39 $2x{y}^{\prime }(x)=2x^3-y(x)$

ODE
$$2x{y}^{\prime }(x)=2x^3-y(x)$$ ODE Classification

[_linear]

Book solution method
Linear ODE

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

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

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

$$\{y\left(x\right)=\frac{2x^3}{7}+\mathit{\_}\mathit{C}\mathit{1}\frac{1}{\sqrt{x}}\}$$ 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