4.3.2 $x^3+y^{\prime }(x)=x\sqrt{x^4+4y(x)}$

ODE
$$x^3+y^{\prime }(x)=x\sqrt{x^4+4y(x)}$$ ODE Classification

[[_1st_order, _with_linear_symmetries]]

Book solution method
Homogeneous equation, isobaric equation

Mathematica ✓
cpu = 0.0737663 (sec), leaf count = 25

$$\left\{\{y(x)\to 2e^{2c_1}(2e^{2c_1}+x^2)\}\right\}$$

Maple ✓
cpu = 0.072 (sec), leaf count = 47

$$\{1((-\mathit{\_}\mathit{C}\mathit{1}+y\left(x\right))\sqrt{x^4+4y\left(x\right)}-x^2(\mathit{\_}\mathit{C}\mathit{1}+y\left(x\right))){(x^2+\sqrt{x^4+4y\left(x\right)})}^{-1}=0\}$$ Mathematica raw input

DSolve[x^3 + y'[x] == x*Sqrt[x^4 + 4*y[x]],y[x],x]

Mathematica raw output

{{y[x] -> 2*E^(2*C[1])*(2*E^(2*C[1]) + x^2)}}

Maple raw input

dsolve(diff(y(x),x)+x^3 = x*(x^4+4*y(x))^(1/2), y(x),'implicit')

Maple raw output

((-_C1+y(x))*(x^4+4*y(x))^(1/2)-x^2*(_C1+y(x)))/(x^2+(x^4+4*y(x))^(1/2)) = 0