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Question: condition in Laplace transform

Question:condition in Laplace transform

arshl 15 Maple
differential-equations laplace inttrans
July 30 2019
1

Hi. I want to take Laplace transform from differential equation with the final condition(tf).   If the differential equations have initial conditions  it appears in Laplace (for example laplace transform of diff(u,t) is U-s*u(0) that u(0) is initial condition)but for final conditions or boundry conditions What to do ?my equation is
 

> 

restart
> 

with(inttrans)

[addtable, fourier, fouriercos, fouriersin, hankel, hilbert, invfourier, invhilbert, invlaplace, invmellin, laplace, mellin, savetable]

 (1)
> 

``

u is function of x,t and u(x(10),10)=0

> 

u[1] := (1/2)*x^2*t; L1 := laplace(eq1, t, s)

(1/2)*x^2*t

  

eq1/s

 (2)

u(x(10),10)=0; desired output u[1]=x^2(t-10)/2

> 

s1 := u[1]; N[1] := (1/2)*(diff(s1, x))^2+x*(diff(s1, x)); ul[2] := laplace(N[1], t, s); u[2] := invlaplace(ul[2]/s, s, t)

(1/2)*x^2*t

  

(1/2)*x^2*t^2+x^2*t

  

x^2*(s+1)/s^3

  

(1/6)*x^2*t^2*(3+t)

 (3)

I want to apply: u[2](x(10),10)=0

> 

``


 

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