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 = 0.0127628 (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 = 0.02 (sec), leaf count = 35
\[ \left \{ \ln \left ( x \right ) -{\it \_C1}-{\frac {5}{8}\ln \left ( {y \left ( x \right ) {x}^{-{\frac {2}{5}}}} \right ) }+{\frac {5}{8}\ln \left ( {\frac { \left ( y \left ( x \right ) \right ) ^{5}+4\,{x}^{2}}{{x}^{2}}} \right ) }=0 \right \} \] 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),'implicit')
Maple raw output
ln(x)-_C1-5/8*ln(y(x)/x^(2/5))+5/8*ln((y(x)^5+4*x^2)/x^2) = 0