4.15.17 \(x \left (1-x^2 y(x)^4\right ) y'(x)+y(x)=0\)

ODE
\[ x \left (1-x^2 y(x)^4\right ) y'(x)+y(x)=0 \] ODE Classification

[[_homogeneous, `class G`], _rational]

Book solution method
Exact equation, integrating factor

Mathematica
cpu = 0.0194031 (sec), leaf count = 139

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

Maple
cpu = 0.019 (sec), leaf count = 31

\[ \left \{ \ln \relax (x ) -{\it \_C1}-\ln \left ({x}^{2} \left (y \relax (x ) \right ) ^{4}+1 \right ) +2\,\ln \left (y \relax (x ) \sqrt {x} \right ) =0 \right \} \] Mathematica raw input

DSolve[y[x] + x*(1 - x^2*y[x]^4)*y'[x] == 0,y[x],x]

Mathematica raw output

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

Maple raw input

dsolve(x*(1-x^2*y(x)^4)*diff(y(x),x)+y(x) = 0, y(x),'implicit')

Maple raw output

ln(x)-_C1-ln(x^2*y(x)^4+1)+2*ln(y(x)*x^(1/2)) = 0