Solve for the zero-input solution, y_o(t) for the following differential equatio

Question

Solve for the zero-input solution, y_o(t) for the following differential equation using Matlab. (2D^2 + 7D+3) y(t) = (D) x(t) for y_o(0-) = -2 and y^middot_o(0-) = 3. When run, your script should automatically calculate and display the zero-input solution Solve for the zero-input solution, y_o(t) for the following differential equation using Matlab. D(D + 3)y(t) = (D + 1) x(t) for y_o(0-) = 1 and y^middot_o(0-) = -1. when run, your script should automatically calculate and display the zero-input solution Find the impulse response to the following LTIC differential system using Matlab. (D^2 + 4D + 4)h(t) = (2D+4) delta(t) When run your script should automatically calculate and display the impulse response

Explanation / Answer

MATLAB Code :-

clc
clear
syms t
% Question 1 zero input means x(t) = 0
display('Zero input Solution yo(t)')
yt1 = dsolve('2*D2y+7*Dy+3*y=0','y(0)=-2','Dy(0)=3','t')
% Question 2 zero input means x(t) = 0
display('Zero input solution yo(t)')
yt2 = dsolve('D2y+3*y=0','y(0)=1','Dy(0)=-1')
% Question 3 Impluse response
display('Impulse response')
ht = dsolve('D2h+4*Dh+4*h=2*D2+4*D1')

OUTPUT :-

Zero input Solution yo(t)

yt1 =

- (4*exp(-3*t))/5 - (6*exp(-t/2))/5

Zero input solution yo(t)

yt2 =

cos(3^(1/2)*t) - (3^(1/2)*sin(3^(1/2)*t))/3


ht =

C20*exp(-2*t) + C21*t*exp(-2*t)

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