??? Solve the initial value problem using the Laplace transform method x" + 2x' + x...
8. Solve the initial value problem using the Laplace transform method x" + 2x' + x = t + 8(t - 2) x(0) = 0, x'(0) = 1
Solve the following initial value problem using the method of Laplace transform. y" + 2y' +10y = f(t); y(0)= 1, y'(0) = 0, where, f(0) = 10, Ost<10, 20, 10<t.
Use the Laplace transform to solve initial value problems
3. tx" + 2(t-1)x' - 2x = 2, x(0) = 0.
[15] 9. By using the Laplace transform method solve the initial value problem y" - 2y + y = -2 y(0) = 0, 7(0) = 1.
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
16. Solve the IVP with a Laplace transform method x" + 2x' + 2x = e-t, x(0) = 1, x'(0) = 1
Solve the following initial boundary value problem using Laplace transform.$$ \begin{aligned} u_{t} &=u_{x x}+t e^{-\pi^{2} t} \sin (\pi x), & 0<x<1, t="">0 \\ u(0, t)=0, & u(1, t)=0, & t>0 & \\ u(x, 0) &=\sin (2 \pi x) & & \end{aligned} $$
(1) Use the Laplace transform method to solve the initial value problem x + 2y. V=x+', (0) = 0 (0) -0. (Note that once you find either (t) or y(t), the other can be computed from the syste of ODE.) ISA - X-xo) = x +2Y ST-y(0) = X te 15.- 2 1 X(5-)-2Y=0 lo -2ts(s)
In this exercise we will use the Laplace transform to solve the following initial value problem: y"-2y'+ 17y-17, y(0)=0, y'(0)=1 (1) First, using Y for the Laplace transform of y(t), i.e., Y =L(y(t)), find the equation obtained by taking the Laplace transform of the initial value problem (2) Next solve for Y= (3) Finally apply the inverse Laplace transform to find y(t)
o use Laplace Transform method to solve Initial Value Problem y" - 8y' & 1by = t² est y (8) = 1 y(0)=4