Advanced Search

Question: Nonhomogeneous ODE

Question:Nonhomogeneous ODE

Parham2016 70 Maple
dsolve nonhomogeneous
February 27 2016
1

 

``

``

M := diff(T(r), r, r)+(diff(T(r), r))/r+u*(-8*B*U+N)*T(r)+P*(r^4+r^2) = 0

diff(diff(T(r), r), r)+(diff(T(r), r))/r+u*(-8*B*U+N)*T(r)+P*(r^4+r^2) = 0

 (1)

``

dsolve(M)

T(r) = BesselJ(0, (-8*B*U*u+N*u)^(1/2)*r)*_C2+BesselY(0, (-8*B*U*u+N*u)^(1/2)*r)*_C1+64*P*(1+(r^2+1)*(B*U-(1/8)*N)^2*r^2*u^2+2*(B*U-(1/8)*N)*(r^2+1/4)*u)/(u^3*(8*B*U-N)^3)

 (2)

``

ics := (D(T))(0) = 0

(D(T))(0) = 0

 (3)

``

dsolve({M, ics})

T(r) = 64*P*(1+(r^2+1)*(B*U-(1/8)*N)^2*r^2*u^2+2*(B*U-(1/8)*N)*(r^2+1/4)*u)/(u^3*(8*B*U-N)^3)

 (4)

``

 

Download nonhomogeneous_Solution.mwnonhomogeneous_Solution.mw

 

Hi everybody,

I want to solve this nonhomogeneous equation. Please tell me if it is true? I'm sure the BesselJ will not be disapper when the boundary condition is exerted... But the final solution showes the opposite one. BesselY must be disappear, because the boundary condition says in r=0, the solution is finite....

 

Thanks a lot.

 
Please Wait...