Advanced Search

Question: dsolve an ode with parametric boundary

Question:dsolve an ode with parametric boundary

mehdi jafari 764 Maple 2022
ode dsolve differential-equations
February 13 2023
1

i have on ode with some parameters. it is ok and it is solved. but when i substitute the parameter itself, it is not solved, can i use any assumption to solve this? tnx for the help.

> 

restart
> 

ode := diff(T(x), x, x)+q/k = 0

diff(diff(T(x), x), x)+q/k = 0

 (1)
> 

dsolve(ode)

T(x) = -(1/2)*q*x^2/k+_C1*x+_C2

 (2)
> 

ics1 := -k*(D(T))(0) = h[1]*(T[inf1]-T(0)), -k*(D(T))(0.5e-1) = h[2]*(T(0.5e-1)-T[inf2])

-k*(D(T))(0) = h[1]*(T[inf1]-T(0)), -k*(D(T))(0.5e-1) = h[2]*(T(0.5e-1)-T[inf2])

 (3)
> 

dsolve({ics1, ode})

T(x) = -(1/2)*q*x^2/k-(1/40)*h[1]*(800*k*T[inf1]*h[2]-800*k*T[inf2]*h[2]-40*k*q-q*h[2])*x/((20*k*h[1]+20*k*h[2]+h[1]*h[2])*k)+(1/40)*(800*k*T[inf1]*h[1]+800*k*T[inf2]*h[2]+40*T[inf1]*h[1]*h[2]+40*k*q+q*h[2])/(20*k*h[1]+20*k*h[2]+h[1]*h[2])

 (4)
> 

ics2 := -k*(D(T))(0) = h[1]*(T[inf1]-T(0)), -k*(D(T))(L) = h[2]*(T(L)-T[inf2])

-k*(D(T))(0) = h[1]*(T[inf1]-T(0)), -k*(D(T))(L) = h[2]*(T(L)-T[inf2])

 (5)
> 

dsolve({ics2, ode})

Error, (in dsolve) found differentiated functions with same name but depending on different arguments in the given DE system: {T(L), T(x)}

  
> 

``

Download ExactSol.mw
Please Wait...