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

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NIRUPAM SAHOO 2021 年 9 月 11 日
コメント済み: NIRUPAM SAHOO 2021 年 9 月 12 日 ##### 1 件のコメント表示非表示 なし
NIRUPAM SAHOO 2021 年 9 月 12 日
please anyone solve this . here u and v are functions of r.

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### 回答 (2 件)

Wan Ji 2021 年 9 月 12 日
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 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
assume(r, 'real')
du = diff(u);
dv = diff(v);
left1 = diff(r^(N-1)*du^3)
left1(r) = right1 = r^(N-1) * sqrt(u) * sqrt(v) / (3*r^(2/3) * sqrt(1 + 9*squiggle^(10/9)/(10*(3*N-2)^(1/3))))
right1(r) = left2 = diff(r^(N-1)*dv^3)
left2(r) = right2 = r^(N-1) * u * v / (3*r^(2/3))
right2(r) = eqn1 = left1 == right1
eqn1(r) = eqn2 = left2 == right2
eqn2(r) = ic = [u(0) == 1, v(0) == 1, du(0) == 0, dv(0) == 0]
ic = sol = dsolve([eqn1, eqn2, ic])
Warning: Unable to find symbolic solution.
sol = [ empty sym ]
string(eqn1)
ans = "3*r^(N - 1)*diff(u(r), r)^2*diff(u(r), r, r) + r^(N - 2)*(N - 1)*diff(u(r), r)^3 == (r^(N - 1)*u(r)^(1/2)*v(r)^(1/2))/(3*r^(2/3)*((9*squiggle^(10/9))/(10*(3*N - 2)^(1/3)) + 1)^(1/2))"
string(eqn2)
ans = "3*r^(N - 1)*diff(v(r), r)^2*diff(v(r), r, r) + r^(N - 2)*(N - 1)*diff(v(r), r)^3 == (r^(N - 1)*u(r)*v(r))/(3*r^(2/3))"
string(ic)
ans = 1×4 string array
"u(0) == 1" "v(0) == 1" "subs(diff(u(r), r), r, 0) == 0" "subs(diff(v(r), r), r, 0) == 0"
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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NIRUPAM SAHOO 2021 年 9 月 12 日
syms p(t) m(t) t Y
Eqns = [diff((t^(100-1))*(diff(p(t),t))) == (t^(100-1))*(t-1)*exp(t)*p(t)*m(t);
diff((t^(100-1))*(diff(m(t),t))) == (t^(100-1))*(t-1)*exp(t)*p(t)^(1/2)*m(t)^(1/2)]
[DEsys,Subs] = odeToVectorField(Eqns);
DEFcn = matlabFunction(DEsys, 'Vars',{t,Y});
tspan = [0,100];
y0 = [0 0 0 0];
[t,Y] = ode45(DEFcn, tspan, y0);
plot(t,Y)

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R2021a

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