##### 4.13.11 $$\left (x^4+y(x)^2\right ) y'(x)=4 x^3 y(x)$$

ODE
$\left (x^4+y(x)^2\right ) y'(x)=4 x^3 y(x)$ ODE Classiﬁcation

[[_homogeneous, class G], _rational]

Book solution method
Exact equation, integrating factor

Mathematica
cpu = 0.319878 (sec), leaf count = 53

$\left \{\left \{y(x)\to \frac {1}{2} \left (c_1-\sqrt {4 x^4+c_1{}^2}\right )\right \},\left \{y(x)\to \frac {1}{2} \left (\sqrt {4 x^4+c_1{}^2}+c_1\right )\right \}\right \}$

Maple
cpu = 0.311 (sec), leaf count = 67

$\left [y \left (x \right ) = \left (\frac {2 x^{2}+\textit {\_C1} -\sqrt {4 x^{4}+\textit {\_C1}^{2}}}{2 x^{2}}-1\right ) x^{2}, y \left (x \right ) = \left (\frac {2 x^{2}+\textit {\_C1} +\sqrt {4 x^{4}+\textit {\_C1}^{2}}}{2 x^{2}}-1\right ) x^{2}\right ]$ Mathematica raw input

DSolve[(x^4 + y[x]^2)*y'[x] == 4*x^3*y[x],y[x],x]

Mathematica raw output

{{y[x] -> (C[1] - Sqrt[4*x^4 + C[1]^2])/2}, {y[x] -> (C[1] + Sqrt[4*x^4 + C[1]^2
])/2}}

Maple raw input

dsolve((x^4+y(x)^2)*diff(y(x),x) = 4*x^3*y(x), y(x))

Maple raw output

[y(x) = (1/2/x^2*(2*x^2+_C1-(4*x^4+_C1^2)^(1/2))-1)*x^2, y(x) = (1/2/x^2*(2*x^2+
_C1+(4*x^4+_C1^2)^(1/2))-1)*x^2]