ODE
\[ 4 x^2 y(x)^2 y'(x)^2=\left (x^2+y(x)^2\right )^2 \] ODE Classification
[[_homogeneous, `class A`], _rational, _Bernoulli]
Book solution method
No Missing Variables ODE, Solve for \(y'\)
Mathematica ✓
cpu = 0.336587 (sec), leaf count = 97
\[\left \{\left \{y(x)\to -\sqrt {x} \sqrt {x+c_1}\right \},\left \{y(x)\to \sqrt {x} \sqrt {x+c_1}\right \},\left \{y(x)\to -\frac {\sqrt {-x^3+3 c_1}}{\sqrt {3} \sqrt {x}}\right \},\left \{y(x)\to \frac {\sqrt {-x^3+3 c_1}}{\sqrt {3} \sqrt {x}}\right \}\right \}\]
Maple ✓
cpu = 0.092 (sec), leaf count = 75
\[\left [y \left (x \right ) = -\frac {\sqrt {3}\, \sqrt {x \left (-x^{3}+3 \textit {\_C1} \right )}}{3 x}, y \left (x \right ) = \frac {\sqrt {3}\, \sqrt {x \left (-x^{3}+3 \textit {\_C1} \right )}}{3 x}, y \left (x \right ) = \sqrt {x \textit {\_C1} +x^{2}}, y \left (x \right ) = -\sqrt {x \textit {\_C1} +x^{2}}\right ]\] Mathematica raw input
DSolve[4*x^2*y[x]^2*y'[x]^2 == (x^2 + y[x]^2)^2,y[x],x]
Mathematica raw output
{{y[x] -> -(Sqrt[x]*Sqrt[x + C[1]])}, {y[x] -> Sqrt[x]*Sqrt[x + C[1]]}, {y[x] -> -(Sqrt[-x^3 + 3*C[1]]/(Sqrt[3]*Sqrt[x]))}, {y[x] -> Sqrt[-x^3 + 3*C[1]]/(Sqrt[3]*Sqrt[x])}}
Maple raw input
dsolve(4*x^2*y(x)^2*diff(y(x),x)^2 = (x^2+y(x)^2)^2, y(x))
Maple raw output
[y(x) = -1/3/x*3^(1/2)*(x*(-x^3+3*_C1))^(1/2), y(x) = 1/3/x*3^(1/2)*(x*(-x^3+3*_C1))^(1/2), y(x) = (_C1*x+x^2)^(1/2), y(x) = -(_C1*x+x^2)^(1/2)]