4.23.10 \(x^2 \left (y'(x)^6+3 y(x)^4+3 y(x)^2+1\right )=a^2\)

ODE
\[ x^2 \left (y'(x)^6+3 y(x)^4+3 y(x)^2+1\right )=a^2 \] ODE Classification

[_rational]

Book solution method
Missing Variables ODE, Dependent variable missing, Solve for \(x\)

Mathematica
cpu = 36.1805 (sec), leaf count = 0 , could not solve

DSolve[x^2*(1 + 3*y[x]^2 + 3*y[x]^4 + Derivative[1][y][x]^6) == a^2, y[x], x]

Maple
cpu = 6.672 (sec), leaf count = 0 , could not solve

dsolve(x^2*(diff(y(x),x)^6+3*y(x)^4+3*y(x)^2+1) = a^2, y(x),'implicit')

Mathematica raw input

DSolve[x^2*(1 + 3*y[x]^2 + 3*y[x]^4 + y'[x]^6) == a^2,y[x],x]

Mathematica raw output

DSolve[x^2*(1 + 3*y[x]^2 + 3*y[x]^4 + Derivative[1][y][x]^6) == a^2, y[x], x]

Maple raw input

dsolve(x^2*(diff(y(x),x)^6+3*y(x)^4+3*y(x)^2+1) = a^2, y(x),'implicit')

Maple raw output

dsolve(x^2*(diff(y(x),x)^6+3*y(x)^4+3*y(x)^2+1) = a^2, y(x),'implicit')