# Question:How to do the algebraic extension in Maple or how can I eliminate algebraic parameters in Maple?

## Question:How to do the algebraic extension in Maple or how can I eliminate algebraic parameters in Maple?

Maple

If I have an equation:

-2*a[0]*((x^3*a[1] + 42)*diff(y(x), x, x) - 6*y(x)*x*a[1])*sqrt(-a[0]*(a[1]^2 + 3)) - 3*x^2*((1/3*a[1]^3 + a[0] + a[1])*x + (8*a[1]^2 + 24)*a[0])*diff(y(x), x, x)

I want to obtain a differential algebraic equation for y(x)without the parameters a[1] and a[0]. My idea is to first compute the derivative of U to get:

V:=-2*a[0]*(3*x^2*a[1]*diff(y(x), x, x) + (x^3*a[1] + 42)*diff(y(x), x, x, x) - 6*diff(y(x), x)*x*a[1] - 6*a[1]*y(x))*sqrt(-a[0]*(a[1]^2 + 3)) - 6*x*((1/3*a[1]^3 + a[0] + a[1])*x + (8*a[1]^2 + 24)*a[0])*diff(y(x), x, x) - 3*x^2*(1/3*a[1]^3 + a[0] + a[1])*diff(y(x), x, x) - 3*x^2*((1/3*a[1]^3 + a[0] + a[1])*x + (8*a[1]^2 + 24)*a[0])*diff(y(x), x, x, x)

Then, compute the resultant: resultant(U,V,a[0]). However, since a[0] is algebraic, we cannot compute the resultant directly. I want to substitute:

algsubs((−a[0](a[1]2+3))2=c2,U)

Then, eliminate c, a[0], and a[1] using the resultant. However, I find that this substitution command does not work. Is there a method to help eliminate the parameters a[0]and a[1]?

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