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

[NIRUPAM SAHOO]

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

Answer 1

[Wan Ji]

Hey friend

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

Answer 2

[Walter Roberson]

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.

[NIRUPAM SAHOO]

" I was not able to figure out what is being raised to 10/9 . I used squiggle instead."

here r^(10/9)

[NIRUPAM SAHOO]

if i go through the ode45 then what happend

[Wan Ji]

@NIRUPAM SAHOO You try it, then you know. No try, only god knows

[NIRUPAM SAHOO]

i try wait for some time.

[NIRUPAM SAHOO]

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)

## i write this but the graph does not shows . please help me