please anyone solve this . here u and v are functions of r.

# how to write to solve this type of system of equations ?

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### Answers (2)

Wan Ji
on 12 Sep 2021

Hey friend

Just expand the left items of the two equations, extract u'' and v'', then an ode45 solver is there for you.

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Walter Roberson
on 12 Sep 2021

Edited: Walter Roberson
on 12 Sep 2021

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

assume(r, '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])

string(eqn1)

string(eqn2)

string(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.

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