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 = 0.0134071 (sec), leaf count = 97
\[\left \{\left \{y(x)\to -\sqrt {x} \sqrt {c_1+x}\right \},\left \{y(x)\to \sqrt {x} \sqrt {c_1+x}\right \},\left \{y(x)\to -\frac {\sqrt {3 c_1-x^3}}{\sqrt {3} \sqrt {x}}\right \},\left \{y(x)\to \frac {\sqrt {3 c_1-x^3}}{\sqrt {3} \sqrt {x}}\right \}\right \}\]
Maple ✓
cpu = 0.015 (sec), leaf count = 32
\[ \left \{ \left ( y \left ( x \right ) \right ) ^{2}- \left ( x+{\it \_C1} \right ) x=0, \left ( y \left ( x \right ) \right ) ^{2}+{\frac {{x}^{2}}{3}}-{\frac {{\it \_C1}}{x}}=0 \right \} \] 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),'implicit')
Maple raw output
y(x)^2-(x+_C1)*x = 0, y(x)^2+1/3*x^2-1/x*_C1 = 0