ZILLDIFFEQMODAP11 7.2.037.MI.
Use the Laplace transform to solve the given initial-value problem.
y' + 5y = e3t, y(0) = 2
y(t) = _______
ZILLDIFFEQMODAP11 7.2.037.MI. Use the Laplace transform to solve the given initial-value problem.
ZILLDIFFEQMODAP11 7.5.007.MI. Use the Laplace transform to solve the given initial-value problem. y" + 5y' = δ(t - 1), y(0) = 0, y'(0) = 1 y(t) = _______
9. DETAILS ZILLDIFFEQMODAP11 7.2.037.MI. MY NOTES ASK YOUR TEACHER Use the Laplace transform to solve the given initial-value problem. y' + 5y = e6t, y(0) = 2 y(t) =
Use the Laplace transform to solve the given initial-value problem. y" + 6y' + 5y = 0, y(0) = 1, y'(O) = 0 y(t) =
17. Use the Laplace transform to solve the initial value problem: y" + 4y' + 4y = 2e-, y(0) = 1, (O) = 3. 18. Use the Laplace transform to solve the initial value problem: 4y" – 4y + 5y = 4 sin(t) – 4 cos(1), y(0) = 0, y(0) = 11/17.
(4 points) Use the Laplace transform to solve the following initial value problem: y" – 2y + 5y = 0 y(0) = 0, y'(0) = 8 First, using Y for the Laplace transform of y(t), i.e., Y = L{y(t)}| find the equation you get by taking the Laplace transform of the differential equation = 01 Now solve for Y(3) By completing the square in the denominator and inverting the transform, find g(t) =
Use the Laplace transform to solve the given initial-value problem.y'' − 5y' = 8e4t − 4e−t, y(0) = 1, y'(0) = −1y(t) =
Use the Laplace transform to solve the given initial-value problem.y'' − 5y' = 8e4t − 4e−t, y(0) = 1, y'(0) = −1y(t) =
Use the Laplace transform to solve the given initial-value problem.$$ y^{\prime}+y=f(t), \quad y(0)=0, \text { where } f(t)=\left\{\begin{array}{rr} 0, & 0 \leq t<1 \\ 5, & t \geq 1 \end{array}\right. $$
13. Use the Laplace transform to solve the initial value problem: (&pts) y" - 6y' + 5y = 3e, y(0) = 2, 7(0) = 3
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)