4.14.37 \(y(x) \left (2 y(x)^2+1\right ) y'(x)=x \left (2 x^2+1\right )\)

ODE
\[ y(x) \left (2 y(x)^2+1\right ) y'(x)=x \left (2 x^2+1\right ) \] ODE Classification

[_separable]

Book solution method
Separable ODE, Neither variable missing

Mathematica
cpu = 0.0118461 (sec), leaf count = 151

\[\left \{\left \{y(x)\to -\frac {\sqrt {-\sqrt {8 c_1+4 x^4+4 x^2+1}-1}}{\sqrt {2}}\right \},\left \{y(x)\to \frac {\sqrt {-\sqrt {8 c_1+4 x^4+4 x^2+1}-1}}{\sqrt {2}}\right \},\left \{y(x)\to -\frac {\sqrt {\sqrt {8 c_1+4 x^4+4 x^2+1}-1}}{\sqrt {2}}\right \},\left \{y(x)\to \frac {\sqrt {\sqrt {8 c_1+4 x^4+4 x^2+1}-1}}{\sqrt {2}}\right \}\right \}\]

Maple
cpu = 0.009 (sec), leaf count = 23

\[ \left \{ {x}^{4}- \left (y \relax (x ) \right ) ^{4}+{x}^{2}- \left (y \relax (x ) \right ) ^{2}+{\it \_C1}=0 \right \} \] Mathematica raw input

DSolve[y[x]*(1 + 2*y[x]^2)*y'[x] == x*(1 + 2*x^2),y[x],x]

Mathematica raw output

{{y[x] -> -(Sqrt[-1 - Sqrt[1 + 4*x^2 + 4*x^4 + 8*C[1]]]/Sqrt[2])}, {y[x] -> Sqrt
[-1 - Sqrt[1 + 4*x^2 + 4*x^4 + 8*C[1]]]/Sqrt[2]}, {y[x] -> -(Sqrt[-1 + Sqrt[1 + 
4*x^2 + 4*x^4 + 8*C[1]]]/Sqrt[2])}, {y[x] -> Sqrt[-1 + Sqrt[1 + 4*x^2 + 4*x^4 + 
8*C[1]]]/Sqrt[2]}}

Maple raw input

dsolve(y(x)*(1+2*y(x)^2)*diff(y(x),x) = x*(2*x^2+1), y(x),'implicit')

Maple raw output

x^4-y(x)^4+x^2-y(x)^2+_C1 = 0