Question: How check this pde ?

my solution is a little bit long which when i click on pdetest command i wait at least more than a hour but still is runing and i don't get any result and not give me error , which i don't know my result is true or not so How i can find that my pde by this solution it will be zero or not ?

restart

with(PDEtools)

with(LinearAlgebra)

NULL

with(SolveTools)

undeclare(prime)

`There is no more prime differentiation variable; all derivatives will be displayed as indexed functions`

(1)

declare(u(x, y, t))

u(x, y, t)*`will now be displayed as`*u

(2)

declare(f(x, y, t))

f(x, y, t)*`will now be displayed as`*f

(3)

pde := diff(u(x, y, t), t)-(diff(diff(u(x, y, t), `$`(x, 4))+5*u(x, y, t)*(diff(u(x, y, t), `$`(x, 2)))+(5/3)*u(x, y, t)^3+5*(diff(u(x, y, t), x, y)), x))-5*u(x, y, t)*(diff(u(x, y, t), y))+5*(int(diff(u(x, y, t), `$`(y, 2)), x))-5*(diff(u(x, y, t), x))*(int(diff(u(x, y, t), y), x))

diff(u(x, y, t), t)-(diff(diff(diff(diff(diff(u(x, y, t), x), x), x), x), x))-5*(diff(u(x, y, t), x))*(diff(diff(u(x, y, t), x), x))-5*u(x, y, t)*(diff(diff(diff(u(x, y, t), x), x), x))-5*u(x, y, t)^2*(diff(u(x, y, t), x))-5*(diff(diff(diff(u(x, y, t), x), x), y))-5*u(x, y, t)*(diff(u(x, y, t), y))+5*(int(diff(diff(u(x, y, t), y), y), x))-5*(diff(u(x, y, t), x))*(int(diff(u(x, y, t), y), x))

(4)

pde_nonlinear, pde_linear := selectremove(proc (term) options operator, arrow; has((eval(term, u(x, y, t) = a*u(x, y, t)))/a, a) end proc, pde)

-5*(diff(u(x, y, t), x))*(diff(diff(u(x, y, t), x), x))-5*u(x, y, t)*(diff(diff(diff(u(x, y, t), x), x), x))-5*u(x, y, t)^2*(diff(u(x, y, t), x))-5*u(x, y, t)*(diff(u(x, y, t), y))-5*(diff(u(x, y, t), x))*(int(diff(u(x, y, t), y), x)), diff(u(x, y, t), t)-(diff(diff(diff(diff(diff(u(x, y, t), x), x), x), x), x))-5*(diff(diff(diff(u(x, y, t), x), x), y))+5*(int(diff(diff(u(x, y, t), y), y), x))

(5)

thetai := t*w[i]+y*p[i]+x

t*w[i]+y*p[i]+x

(6)

eqw := w[i] = -5*p[i]^2

w[i] = -5*p[i]^2

(7)

Bij := proc (i, j) options operator, arrow; (-6*p[i]-6*p[j])/(p[i]-p[j])^2 end proc

proc (i, j) options operator, arrow; (-6*p[i]-6*p[j])/(p[i]-p[j])^2 end proc

(8)

NULL

theta1 := normal(eval(eval(thetai, eqw), i = 1)); theta2 := normal(eval(eval(thetai, eqw), i = 2))

-5*t*p[1]^2+y*p[1]+x

 

-5*t*p[2]^2+y*p[2]+x

(9)

eqf := f(x, y, t) = (-5*t*p[1]^2+y*p[1]+x)*(-5*t*p[2]^2+y*p[2]+x)-(6*(p[1]+p[2]))/(p[1]-p[2])^2

f(x, y, t) = (-5*t*p[1]^2+y*p[1]+x)*(-5*t*p[2]^2+y*p[2]+x)-6*(p[1]+p[2])/(p[1]-p[2])^2

(10)

eq17 := u(x, y, t) = 6*(diff(diff(f(x, y, t), x), x))/f(x, y, t)-6*(diff(f(x, y, t), x))^2/f(x, y, t)^2

u(x, y, t) = 6*(diff(diff(f(x, y, t), x), x))/f(x, y, t)-6*(diff(f(x, y, t), x))^2/f(x, y, t)^2

(11)

eqt := eval(eq17, eqf)

u(x, y, t) = 12/((-5*t*p[1]^2+y*p[1]+x)*(-5*t*p[2]^2+y*p[2]+x)-6*(p[1]+p[2])/(p[1]-p[2])^2)-6*(-5*t*p[1]^2-5*t*p[2]^2+y*p[1]+y*p[2]+2*x)^2/((-5*t*p[1]^2+y*p[1]+x)*(-5*t*p[2]^2+y*p[2]+x)-6*(p[1]+p[2])/(p[1]-p[2])^2)^2

(12)

``

pdetest(eqt, pde)

NULL

Download test.mw

Please Wait...