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]