ODE
\[ y(x) \left (a+x^2+y(x)^2\right ) y'(x)=x \left (a-x^2-y(x)^2\right ) \] ODE Classification
[_exact, _rational]
Book solution method
Exact equation
Mathematica ✓
cpu = 0.523207 (sec), leaf count = 149
\[\left \{\left \{y(x)\to -\sqrt {-\sqrt {a^2+4 a x^2+4 c_1}-a-x^2}\right \},\left \{y(x)\to \sqrt {-\sqrt {a^2+4 a x^2+4 c_1}-a-x^2}\right \},\left \{y(x)\to -\sqrt {\sqrt {a^2+4 a x^2+4 c_1}-a-x^2}\right \},\left \{y(x)\to \sqrt {\sqrt {a^2+4 a x^2+4 c_1}-a-x^2}\right \}\right \}\]
Maple ✓
cpu = 0.055 (sec), leaf count = 125
\[\left [y \left (x \right ) = \sqrt {-x^{2}-a -\sqrt {4 a \,x^{2}+a^{2}-4 \textit {\_C1}}}, y \left (x \right ) = \sqrt {-x^{2}-a +\sqrt {4 a \,x^{2}+a^{2}-4 \textit {\_C1}}}, y \left (x \right ) = -\sqrt {-x^{2}-a -\sqrt {4 a \,x^{2}+a^{2}-4 \textit {\_C1}}}, y \left (x \right ) = -\sqrt {-x^{2}-a +\sqrt {4 a \,x^{2}+a^{2}-4 \textit {\_C1}}}\right ]\] Mathematica raw input
DSolve[y[x]*(a + x^2 + y[x]^2)*y'[x] == x*(a - x^2 - y[x]^2),y[x],x]
Mathematica raw output
{{y[x] -> -Sqrt[-a - x^2 - Sqrt[a^2 + 4*a*x^2 + 4*C[1]]]}, {y[x] -> Sqrt[-a - x^2 - Sqrt[a^2 + 4*a*x^2 + 4*C[1]]]}, {y[x] -> -Sqrt[-a - x^2 + Sqrt[a^2 + 4*a*x^2 + 4*C[1]]]}, {y[x] -> Sqrt[-a - x^2 + Sqrt[a^2 + 4*a*x^2 + 4*C[1]]]}}
Maple raw input
dsolve((a+x^2+y(x)^2)*y(x)*diff(y(x),x) = x*(a-x^2-y(x)^2), y(x))
Maple raw output
[y(x) = (-x^2-a-(4*a*x^2+a^2-4*_C1)^(1/2))^(1/2), y(x) = (-x^2-a+(4*a*x^2+a^2-4*_C1)^(1/2))^(1/2), y(x) = -(-x^2-a-(4*a*x^2+a^2-4*_C1)^(1/2))^(1/2), y(x) = -(-x^2-a+(4*a*x^2+a^2-4*_C1)^(1/2))^(1/2)]