melika mokhtari

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These are questions asked by melika mokhtari

Hello Everyone

I have solved the equation below numerically and now I want to integral p(x)

ode := diff((b+5)*((1/6)*(diff(p(x), x))*h^3+(1/2)*c*h^2)/(b+2)+De^2*((1/10)*(diff(p(x), x))^3*h^5+c^2*(diff(p(x), x))*h^3+(1/2)*c*(diff(p(x), x))^2*h^4+c^3*h^2)/(b+2), x)+diff(h, x) = 0

ics := p(0) = 0, p(1) = 0;
                   ics := p(0) = 0, p(1) = 0
solnum := dsolve({ics, ode}, numeric, method = bvp, maxmesh = 600);
                solnum := proc(x_bvp)  ...  end;
odeplot(solnum, 0 .. 1)

but when I write evalf(int(p,0..1)) I get this result:int(p,0..1). What should I do to have the value?

Hi,

i am trying to solve a differential equation numercially but since it is second degree,I can not achieve the proper answer.What should I do?

thank you
diff1.mw
 

restart

h := 1-.8*x+.5*(x^2-x)

1-1.3*x+.5*x^2

(1)

z := 3^(3/2)*(((2+k*De^2*(diff(p(x), x))^2*h^2)^3*h^2+108*k*De^2)/k)^(1/2)

3*3^(1/2)*(((2+k*De^2*(diff(p(x), x))^2*(1-1.3*x+.5*x^2)^2)^3*(1-1.3*x+.5*x^2)^2+108*k*De^2)/k)^(1/2)

(2)

c := (1/6)*((-54*De+z)*k^2*h^2)^(1/3)/(k*De*h)-(1/2)*h*(2+k*De^2*(diff(p(x), x))^2*h^2)/(De*((-54*De+z)*k^2*h^2)^(1/3))-(1/2)*h*(diff(p(x), x))

(1/6)*((-54*De+3*3^(1/2)*(((2+k*De^2*(diff(p(x), x))^2*(1-1.3*x+.5*x^2)^2)^3*(1-1.3*x+.5*x^2)^2+108*k*De^2)/k)^(1/2))*k^2*(1-1.3*x+.5*x^2)^2)^(1/3)/(k*De*(1-1.3*x+.5*x^2))-(1/2)*(1-1.3*x+.5*x^2)*(2+k*De^2*(diff(p(x), x))^2*(1-1.3*x+.5*x^2)^2)/(De*((-54*De+3*3^(1/2)*(((2+k*De^2*(diff(p(x), x))^2*(1-1.3*x+.5*x^2)^2)^3*(1-1.3*x+.5*x^2)^2+108*k*De^2)/k)^(1/2))*k^2*(1-1.3*x+.5*x^2)^2)^(1/3))-(1/2)*(1-1.3*x+.5*x^2)*(diff(p(x), x))

(3)

ode1 := ((1/2)*c*(diff(p(x), x))^2*h^4+(diff(p(x), x))*c^2*h^3+(1/10)*(diff(p(x), x))*h^5+c^3*h^2)*k*De^2+(1/2)*c*h^2+(1/6)*(diff(p(x), x))*h^3+h = 0

((1/2)*((1/6)*((-54*De+3*3^(1/2)*(((2+k*De^2*(diff(p(x), x))^2*(1-1.3*x+.5*x^2)^2)^3*(1-1.3*x+.5*x^2)^2+108*k*De^2)/k)^(1/2))*k^2*(1-1.3*x+.5*x^2)^2)^(1/3)/(k*De*(1-1.3*x+.5*x^2))-(1/2)*(1-1.3*x+.5*x^2)*(2+k*De^2*(diff(p(x), x))^2*(1-1.3*x+.5*x^2)^2)/(De*((-54*De+3*3^(1/2)*(((2+k*De^2*(diff(p(x), x))^2*(1-1.3*x+.5*x^2)^2)^3*(1-1.3*x+.5*x^2)^2+108*k*De^2)/k)^(1/2))*k^2*(1-1.3*x+.5*x^2)^2)^(1/3))-(1/2)*(1-1.3*x+.5*x^2)*(diff(p(x), x)))*(diff(p(x), x))^2*(1-1.3*x+.5*x^2)^4+(diff(p(x), x))*((1/6)*((-54*De+3*3^(1/2)*(((2+k*De^2*(diff(p(x), x))^2*(1-1.3*x+.5*x^2)^2)^3*(1-1.3*x+.5*x^2)^2+108*k*De^2)/k)^(1/2))*k^2*(1-1.3*x+.5*x^2)^2)^(1/3)/(k*De*(1-1.3*x+.5*x^2))-(1/2)*(1-1.3*x+.5*x^2)*(2+k*De^2*(diff(p(x), x))^2*(1-1.3*x+.5*x^2)^2)/(De*((-54*De+3*3^(1/2)*(((2+k*De^2*(diff(p(x), x))^2*(1-1.3*x+.5*x^2)^2)^3*(1-1.3*x+.5*x^2)^2+108*k*De^2)/k)^(1/2))*k^2*(1-1.3*x+.5*x^2)^2)^(1/3))-(1/2)*(1-1.3*x+.5*x^2)*(diff(p(x), x)))^2*(1-1.3*x+.5*x^2)^3+(1/10)*(diff(p(x), x))*(1-1.3*x+.5*x^2)^5+((1/6)*((-54*De+3*3^(1/2)*(((2+k*De^2*(diff(p(x), x))^2*(1-1.3*x+.5*x^2)^2)^3*(1-1.3*x+.5*x^2)^2+108*k*De^2)/k)^(1/2))*k^2*(1-1.3*x+.5*x^2)^2)^(1/3)/(k*De*(1-1.3*x+.5*x^2))-(1/2)*(1-1.3*x+.5*x^2)*(2+k*De^2*(diff(p(x), x))^2*(1-1.3*x+.5*x^2)^2)/(De*((-54*De+3*3^(1/2)*(((2+k*De^2*(diff(p(x), x))^2*(1-1.3*x+.5*x^2)^2)^3*(1-1.3*x+.5*x^2)^2+108*k*De^2)/k)^(1/2))*k^2*(1-1.3*x+.5*x^2)^2)^(1/3))-(1/2)*(1-1.3*x+.5*x^2)*(diff(p(x), x)))^3*(1-1.3*x+.5*x^2)^2)*k*De^2+(1/2)*((1/6)*((-54*De+3*3^(1/2)*(((2+k*De^2*(diff(p(x), x))^2*(1-1.3*x+.5*x^2)^2)^3*(1-1.3*x+.5*x^2)^2+108*k*De^2)/k)^(1/2))*k^2*(1-1.3*x+.5*x^2)^2)^(1/3)/(k*De*(1-1.3*x+.5*x^2))-(1/2)*(1-1.3*x+.5*x^2)*(2+k*De^2*(diff(p(x), x))^2*(1-1.3*x+.5*x^2)^2)/(De*((-54*De+3*3^(1/2)*(((2+k*De^2*(diff(p(x), x))^2*(1-1.3*x+.5*x^2)^2)^3*(1-1.3*x+.5*x^2)^2+108*k*De^2)/k)^(1/2))*k^2*(1-1.3*x+.5*x^2)^2)^(1/3))-(1/2)*(1-1.3*x+.5*x^2)*(diff(p(x), x)))*(1-1.3*x+.5*x^2)^2+(1/6)*(diff(p(x), x))*(1-1.3*x+.5*x^2)^3+1-1.3*x+.5*x^2 = 0

(4)

ivp := {ode1, p(0) = 0}

{((1/2)*((1/6)*((-54*De+3*3^(1/2)*(((2+k*De^2*(diff(p(x), x))^2*(1-1.3*x+.5*x^2)^2)^3*(1-1.3*x+.5*x^2)^2+108*k*De^2)/k)^(1/2))*k^2*(1-1.3*x+.5*x^2)^2)^(1/3)/(k*De*(1-1.3*x+.5*x^2))-(1/2)*(1-1.3*x+.5*x^2)*(2+k*De^2*(diff(p(x), x))^2*(1-1.3*x+.5*x^2)^2)/(De*((-54*De+3*3^(1/2)*(((2+k*De^2*(diff(p(x), x))^2*(1-1.3*x+.5*x^2)^2)^3*(1-1.3*x+.5*x^2)^2+108*k*De^2)/k)^(1/2))*k^2*(1-1.3*x+.5*x^2)^2)^(1/3))-(1/2)*(1-1.3*x+.5*x^2)*(diff(p(x), x)))*(diff(p(x), x))^2*(1-1.3*x+.5*x^2)^4+(diff(p(x), x))*((1/6)*((-54*De+3*3^(1/2)*(((2+k*De^2*(diff(p(x), x))^2*(1-1.3*x+.5*x^2)^2)^3*(1-1.3*x+.5*x^2)^2+108*k*De^2)/k)^(1/2))*k^2*(1-1.3*x+.5*x^2)^2)^(1/3)/(k*De*(1-1.3*x+.5*x^2))-(1/2)*(1-1.3*x+.5*x^2)*(2+k*De^2*(diff(p(x), x))^2*(1-1.3*x+.5*x^2)^2)/(De*((-54*De+3*3^(1/2)*(((2+k*De^2*(diff(p(x), x))^2*(1-1.3*x+.5*x^2)^2)^3*(1-1.3*x+.5*x^2)^2+108*k*De^2)/k)^(1/2))*k^2*(1-1.3*x+.5*x^2)^2)^(1/3))-(1/2)*(1-1.3*x+.5*x^2)*(diff(p(x), x)))^2*(1-1.3*x+.5*x^2)^3+(1/10)*(diff(p(x), x))*(1-1.3*x+.5*x^2)^5+((1/6)*((-54*De+3*3^(1/2)*(((2+k*De^2*(diff(p(x), x))^2*(1-1.3*x+.5*x^2)^2)^3*(1-1.3*x+.5*x^2)^2+108*k*De^2)/k)^(1/2))*k^2*(1-1.3*x+.5*x^2)^2)^(1/3)/(k*De*(1-1.3*x+.5*x^2))-(1/2)*(1-1.3*x+.5*x^2)*(2+k*De^2*(diff(p(x), x))^2*(1-1.3*x+.5*x^2)^2)/(De*((-54*De+3*3^(1/2)*(((2+k*De^2*(diff(p(x), x))^2*(1-1.3*x+.5*x^2)^2)^3*(1-1.3*x+.5*x^2)^2+108*k*De^2)/k)^(1/2))*k^2*(1-1.3*x+.5*x^2)^2)^(1/3))-(1/2)*(1-1.3*x+.5*x^2)*(diff(p(x), x)))^3*(1-1.3*x+.5*x^2)^2)*k*De^2+(1/2)*((1/6)*((-54*De+3*3^(1/2)*(((2+k*De^2*(diff(p(x), x))^2*(1-1.3*x+.5*x^2)^2)^3*(1-1.3*x+.5*x^2)^2+108*k*De^2)/k)^(1/2))*k^2*(1-1.3*x+.5*x^2)^2)^(1/3)/(k*De*(1-1.3*x+.5*x^2))-(1/2)*(1-1.3*x+.5*x^2)*(2+k*De^2*(diff(p(x), x))^2*(1-1.3*x+.5*x^2)^2)/(De*((-54*De+3*3^(1/2)*(((2+k*De^2*(diff(p(x), x))^2*(1-1.3*x+.5*x^2)^2)^3*(1-1.3*x+.5*x^2)^2+108*k*De^2)/k)^(1/2))*k^2*(1-1.3*x+.5*x^2)^2)^(1/3))-(1/2)*(1-1.3*x+.5*x^2)*(diff(p(x), x)))*(1-1.3*x+.5*x^2)^2+(1/6)*(diff(p(x), x))*(1-1.3*x+.5*x^2)^3+1-1.3*x+.5*x^2 = 0, p(0) = 0}

(5)

dsolve(ivp, p(x), numeric, parameters = [k, De])

Error, (in dsolve/numeric/make_proc) Could not convert to an explicit first order system due to 'RootOf'

 

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