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]