##### 4.15.18 $$\left (x^2-y(x)^5\right ) y'(x)=2 x y(x)$$

ODE
$\left (x^2-y(x)^5\right ) y'(x)=2 x y(x)$ ODE Classiﬁcation

[[_homogeneous, class G], _rational]

Book solution method
Exact equation, integrating factor

Mathematica
cpu = 0.322028 (sec), leaf count = 116

$\left \{\left \{y(x)\to \text {Root}\left [\text {\#1}^5+4 \text {\#1} c_1+4 x^2\& ,1\right ]\right \},\left \{y(x)\to \text {Root}\left [\text {\#1}^5+4 \text {\#1} c_1+4 x^2\& ,2\right ]\right \},\left \{y(x)\to \text {Root}\left [\text {\#1}^5+4 \text {\#1} c_1+4 x^2\& ,3\right ]\right \},\left \{y(x)\to \text {Root}\left [\text {\#1}^5+4 \text {\#1} c_1+4 x^2\& ,4\right ]\right \},\left \{y(x)\to \text {Root}\left [\text {\#1}^5+4 \text {\#1} c_1+4 x^2\& ,5\right ]\right \}\right \}$

Maple
cpu = 0.45 (sec), leaf count = 25

$\left [y \left (x \right ) = \RootOf \left (x^{8} \textit {\_Z}^{5}+4-{\mathrm e}^{\frac {8 \textit {\_C1}}{5}} \textit {\_Z} \right ) x^{2}\right ]$ Mathematica raw input

DSolve[(x^2 - y[x]^5)*y'[x] == 2*x*y[x],y[x],x]

Mathematica raw output

{{y[x] -> Root[4*x^2 + 4*C[1]*#1 + #1^5 & , 1]}, {y[x] -> Root[4*x^2 + 4*C[1]*#1
 + #1^5 & , 2]}, {y[x] -> Root[4*x^2 + 4*C[1]*#1 + #1^5 & , 3]}, {y[x] -> Root[4
*x^2 + 4*C[1]*#1 + #1^5 & , 4]}, {y[x] -> Root[4*x^2 + 4*C[1]*#1 + #1^5 & , 5]}}

Maple raw input

dsolve((x^2-y(x)^5)*diff(y(x),x) = 2*x*y(x), y(x))

Maple raw output

[y(x) = RootOf(x^8*_Z^5+4-exp(8/5*_C1)*_Z)*x^2]