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 = 25.2657 (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 = 8.748 (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))
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))
Maple raw output
dsolve(x^2*(diff(y(x),x)^6+3*y(x)^4+3*y(x)^2+1) = a^2, y(x))