5) Consider the IVP у"F-у, + 2У = 5x,y(0)= 4, y'(0) =-4. 5) Consider the IVP у"F-у, + 2У = 5x,y(0)=...
(1 point) Consider the IVP У + 3ty — бу %3D 3, у(0) — 0, У (0) — 0 (a) What is the Laplace transform of the differential equation, after being put into standard form? Y'(s) ) Y(s) = |(b) What is the solution to the differential equation? y(t)
QUESTION 4 Consider the CDF 0 у<0 0.5 F(y) = 0.75 0.90 Osy<2 2sy<3 3sy<5 1 Y>5 Find pſy=5) O A. 0.10 B. 0.15 C. 0.25 D.0.25 QUESTION 5 Consider the PM.F
Consider the following IVP
y″ + 5y′ +
y = f (t), y(0) = 3,
y′(0) = 0,
where
f (t) =
{
8
0 ≤ t ≤ 2π
cos(7t)
t > 2π
(a)
Find the Laplace transform F(s) =
ℒ { f (t)} of f (t).
(b)
Find the Laplace transform Y(s) =
ℒ {y(t)} of the solution y(t)
of the above IVP.
Consider the following IVP y" + 5y' + y = f(t), y(0) = 3, y'(0) =...
use method of undetermined coefficients to solve ivp y" - 4y' - 12y = 3e^5x, y(0) = 18/7, y'(0) = -1/7
Find the basis function of the differential equation using
Frobenius method.
b. 2у"+ (1— 2г)y+ (ӕ- 1)у %3D0 c. ()y"(4x 2)y' +2y 0
b. 2у"+ (1— 2г)y+ (ӕ- 1)у %3D0 c. ()y"(4x 2)y' +2y 0
SOLVE #3 AND #4 PLEASE
Use the Laplace transformation to solve the IVP. 1. y"-6y' + 9y-24-9t, y(0)-2, y, (0)-0 2. 9y" - 12y'4y50ey(0)--1,y'(0)2 3. У"-2y'--. 1 2 cos(2t) + 4 sin(2t),y(0)-4,y'(0)-0
Use the Laplace transformation to solve the IVP. 1. y"-6y' + 9y-24-9t, y(0)-2, y, (0)-0 2. 9y" - 12y'4y50ey(0)--1,y'(0)2 3. У"-2y'--. 1 2 cos(2t) + 4 sin(2t),y(0)-4,y'(0)-0
3. (2 pts) The solution of the IVP y = f(y), y(0) = 4 is known to be y(t) = 1+ 9-t. Suppose yz(t) is the solution of the IVP y = f(y), y(2) = 4. Find the solution ya(t).
Solve IVP
23·-=-5x-y dt dy = 4x-y dt x(1) = 0, y(1) = 1
5. Consider the following second order IVP y2y te - t, 0 t1 y(0)/(0) 0 = ( y(t). Transform the above IVP to system of first order (a) Let u(t)y(t) and u2(t) IVP of u and u2. (b) Find y(t) by solving the system with h 0.1 (c) Compare the results to the actual solution y(t) = %et - te 2e t - 2.
5. Consider the following second order IVP y2y te - t, 0 t1 y(0)/(0) 0 =...
Consider the IVP y'' + 3y' + 3y = (1 − u(t − 4)) with y'(0) = 0 and y(0) = 0. Solve the differential equation, and if possible, provide a graph