Let y(t) = (1 + t)^2 solution of the
differential equation y´´ (t) + p (t) y´ (t) + q (t) y (t) = 0
(*)
If the Wronskian of two solutions of (*) equals three.
(a) ffind p(t) and q(t)
(b) Solve y´´ (t) + p (t) y´ (t) + q (t) y (t) = 1 + t
find the general solution of the given differential
equation.
1. y'' + y = tan t, 0 < t < π/2
2. y'' + 4y' + 4y = t-2 e-2t , t >
0
find the solution of the given initial value problem.
3. y'' + y' − 2y = 2t, y(0) = 0, y'(0) = 1
1. The differential equation y''+4y=f(t) and
y'(0)=y(0)=0
a. Find the transfer function and impulse response.
b. If f(t)=u(t)-u(t-1). Find the y(t) by convolution and Laplace
techniques. u(t) is unit step function.
c. If f(t)= cos(t) ; find the y(t) by convolution and Laplace
techniques.
2. The differential equation y''+3y'+2y=e^(-3t) and
y'(0)=y(0)=0
a. Find the system transfer function and impulse response.
b. Find the y(t) by convolution and Laplace techniques.
3. y''+3y'+2y=f(t) and
y'(0)=y(0)=0
Plot y(t) without any calculations and write...