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Solve the following initial boundary value problem using Laplace transform.$$ \begin{aligned} u_{t} &=u_{x x}+t e^{-\pi^{2} t} \sin (\pi x), & 0<x<1, t="">0 \\ u(0, t)=0, & u(1, t)=0, & t>0 & \\ u(x, 0) &=\sin (2 \pi x) & & \end{aligned} $$
7. Solve the initial value problem below using the method of Laplace Transform method y" + 4y = 16t2 – 8t + 28, y(0) = 0, y'(0) = 10
There is no need to calculate the Fourier coefficients. Formulas for their calculation should be given indicating specific basis functions and specific integration intervals.
5) Use the method of Laplace transforms to the solve the following boundary value problem IC: u(x, 0) 2 in the following way: a) Apply the Laplace transform in the variable of t to obtain the initial value problem b) Show that U =-+ cie'sz +cge-Vsz s the general solution to the above equation and solve for the constants c and c2 to obtain that c) By taking a power series about the origin and using the identities, sinh iz-...
Solve the initial value problem below using the method of Laplace transforms. y" - 2y' - 3y = 0, y(0) = -1, y' (O) = 17 Click here to view the table of Laplace transforms. Click here to view the table of properties of Laplace transforms y(t) = 1 (Type an exact answer in terms of e.)
Solve the initial value problem below using the method of Laplace transforms. 4ty'' - 6ty' + 6y = 36, y(0) = 6, y'(0) = -1 Click here to view the table of Laplace transforms. Click here to view the table of properties of Laplace transforms. y(t) =
Solve the initial value problem below using the method of Laplace transforms. 2ty" - 5ty' + 5y = 20, y(0) = 4, y'0) = -3 Click here to view the table of Laplace transforms. Click here to view the table of properties of Laplace transforms. y(t) =
In the following problems, solve the given initial value problem using the method of Laplace transforms (a) y" – 7y' + 10y = 9 cost + 7 sint, y(0) = 5, y'(0) = -4 (5 Marks] (b) y" + y = 12 + 2, y(0) = 1, y'(0) = -1 [5 Marks]
Solve the initial value problem below using the method of Laplace transforms. y'' + 4y' + 3y = 45 e 21, y(0) = -6, y'(0) = 21 Click here to view the table of Laplace transforms. Click here to view the table of properties of Laplace transforms. y(t) =
Solve the initial value problem below using the method of Laplace transforms. w" - 2w' + w=5t +6, W( - 2) = 4, w'(-2) = 8 Click here to view the table of Laplace transforms. Click here to view the table of properties of Laplace transforms. w(t) = (Type an exact answer in terms of e.)