4.14.27 \(\left (1-x^4 y(x)^2\right ) y'(x)=x^3 y(x)^3\)

ODE
\[ \left (1-x^4 y(x)^2\right ) y'(x)=x^3 y(x)^3 \] ODE Classification

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

Book solution method
Exact equation, integrating factor

Mathematica
cpu = 0.0178003 (sec), leaf count = 117

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

Maple
cpu = 0.016 (sec), leaf count = 31

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

DSolve[(1 - x^4*y[x]^2)*y'[x] == x^3*y[x]^3,y[x],x]

Mathematica raw output

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

Maple raw input

dsolve((1-x^4*y(x)^2)*diff(y(x),x) = x^3*y(x)^3, y(x),'implicit')

Maple raw output

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