how to write to solve this type of system of equations ?
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回答 (2 件)
Wan Ji 2021 年 9 月 12 日
Just expand the left items of the two equations, extract u'' and v'', then an ode45 solver is there for you.
Walter Roberson 2021 年 9 月 12 日
編集済み: Walter Roberson 2021 年 9 月 12 日
I was not able to figure out what is being raised to 10/9 . I used squiggle instead.
syms u(r) v(r)
syms N squiggle real
du = diff(u);
dv = diff(v);
left1 = diff(r^(N-1)*du^3)
right1 = r^(N-1) * sqrt(u) * sqrt(v) / (3*r^(2/3) * sqrt(1 + 9*squiggle^(10/9)/(10*(3*N-2)^(1/3))))
left2 = diff(r^(N-1)*dv^3)
right2 = r^(N-1) * u * v / (3*r^(2/3))
eqn1 = left1 == right1
eqn2 = left2 == right2
ic = [u(0) == 1, v(0) == 1, du(0) == 0, dv(0) == 0]
sol = dsolve([eqn1, eqn2, ic])
Lack of a symbolic solution means that you would have to do numeric solutions -- but you cannot do a numeric solution to infinity, and you certainly would not get a formula out of it.