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Q2:- Solue the following initial value problem - Y" by t34 so y calab, yco ed...
use the Laplace transform to solue the initial value problem y - 3y +2y = h (t) Y(o)=0 yo(o)=0 where h(t): 0,0 Lt L4 t> 4 { 2
#01) Use separation of variables to solve the following initial value problem x+ye x dy = 0; y(1) = 1 Q2) Solue linear equtians dy - {ysetzt cost
Q2 Given the following heat conduction initial-boundary value problem of a thin homogeneous rod, where ?(?,?) represents the temperature. 9??? = ?? ; 0 < ? < 6; ? > 0; B. C. : ?? (0,?) = 0; ?? (6,?) = 0; ? > 0; I. C. : ?(?, 0) = 12 + 5??? ( ? 6 ?) − 4???(2??); 0 < ? < 6 (a) When ? = 0, what would be the temperature at ? = 3? (Use...
Q2 Given the following heat conduction initial-boundary value
problem of a thin homogeneous rod, where ?(?,?) represents the
temperature. 9??? = ?? ; 0 < ? < 6; ? > 0; B. C. : ??
(0,?) = 0; ?? (6,?) = 0; ? > 0; I. C. : ?(?, 0) = 12 + 5??? ( ?
6 ?) − 4???(2??); 0 < ? < 6 (a) When ? = 0, what would be the
temperature at ? = 3? (Use...
Q2 Given the following heat conduction
initial-boundary value problem of a thin homogeneous rod, where
?(?,?) represents the temperature. 9??? = ?? ; 0 < ? < 6; ?
> 0; B. C. : ?? (0,?) = 0; ?? (6,?) = 0; ? > 0; I. C. : ?(?,
0) = 12 + 5??? ( ? 6 ?) − 4???(2??); 0 < ? < 6 (a) When ? =
0, what would be the temperature at ? = 3? (Use...
So 0<t<5 Using the Laplace transform, solve the initial value problem y' + y = 3 t5 y'(0) = 0. 9
8. Solve the following initial value problem: y" - 6y' + 13y = 0, y(a) = b, y'(c) = d (Note: a, b,c,d will be an a=1 b=7 c=8 d=9]nt ID number)
show solvework in easier way to understand. thanks
Q2 Use Laplace transform to solve the following initial value problem: yty -0 and y(o)-2
Q2 Use Laplace transform to solve the following initial value problem: yty -0 and y(o)-2
For each initial value problem, does Picards's theorem apply? If
so, determine if it guarantees that a solutio exists and is
unique.
Theorem (Picard). Consider the initial value problem dy = f(t,y), dt (IVP) y(to) = Yo- (a) Existence: If f(t,y) is continuous in an open rectangle R = {(t,y) |a<t < b, c < y < d} and (to, Yo) belongs in R, then there exist h > 0 and a solution y = y(t) of (IVP) defined in...
Q2 Given the following heat conduction initial-boundary value problem of a thin homogeneous rod, where u(x, t) represents the temperature. 9uxx = ut; 0 < x < 6; t> 0; B.C.: ux(0,t) = 0; uz(6,t) = 0; t>0; I. C.: u(x,0) = 12 + 5cos (6x) – 4cos(21x); 0<x< 6 (a) When t = 0, what would be the temperature at x = 3? (Use the initial condition.) (b) Determine whether the boundary conditions in this case is Dirichlet, Neumann,...