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 = 0.0127836 (sec), leaf count = 53

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

Maple
cpu = 0.027 (sec), leaf count = 46

\[ \left \{ \ln \relax (x ) -{\it \_C1}+{\frac {1}{2}\ln \left ({\frac {-{x}^{2}+y \relax (x ) }{{x}^{2}}} \right ) }+{\frac {1}{2}\ln \left ({\frac {{x}^{2}+y \relax (x ) }{{x}^{2}}} \right ) }-{\frac {1}{2}\ln \left ({\frac {y \relax (x ) }{{x}^{2}}} \right ) }=0 \right \} \] 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),'implicit')

Maple raw output

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