Question

1) ?²u/?t² = ?²u/?x² in this partial equation, for 0<x<l and t>0 , Boundary Conditions are , u(0,t)=0, u(l,t)=0 and initial value conditions are as follows , u(x,0)=0 and ?u(x,0)/?t =?(x-1/2) where this term is defined as Dirac delta function. Solve the wave eqution above u(x,t) ?

          1) ?²u/?t² = ?²u/?x² in this partial equation, for 0<x<l and t>0 ,

Boundary Conditions are ,

u(0,t)=0, u(l,t)=0

and initial value conditions are as follows ,

u(x,0)=0 and ?u(x,0)/?t =?(x-1/2) where this term is defined as Dirac delta function.

Solve the wave eqution above u(x,t) ?

1) ?²u/?t² = ?²u/?x² in this partial equation, for 0<x<l and t>0 ,

Boundary Conditions are ,

u(0,t)=0, u(l,t)=0

and initial value conditions are as follows ,

u(x,0)=0 and ?u(x,0)/?t =?(x-1/2) where this term is defined as Dirac delta function.

Solve the wave eqution above u(x,t) ?

Added by Logan P.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adi S

06/20/2023

Step 1

We are given a wave equation: $$u_{tt} = 4u_{xx}$$ for $0 < x < L$ and $t > 0$. Boundary conditions: $$u(0, t) = 0, \quad u(L, t) = 0$$ Initial conditions: $$u(x, 0) = 0, \quad u_t(x, 0) = a(x)$$ where $a(x)$ is the Dirac delta function. To solve this Show more…

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In this partial equation, for 0 < x < l and t > 0, the boundary conditions are: U(0, t) = 0 and U(L, t) = 0. The initial value conditions are as follows: u(x, 0) = 0 and a(x) = 0, where this term is defined as the Dirac delta function. Solve the Wave equation.