1) Find y as a function of t if 9y′′+24y′+32y=0,
y(0)=5,y′(0)=8. y(t)=
2) Find y as a function of x if y′′′+16y′=0,
y(0)=−5, y′(0)=−32, y′′(0)=−32. y(x)=
3) Find y as a function of t if 9y′′−12y′+40y=0,
y(1)=5,y′(1)=9. y=
1. Solve the initial value problems
a.) y"-10y'+25y=e^5x, y(0)= 1 and y'(0)= 6
b.) y"+y'-2y=2sin(x), y(0)= 1 and y'(0)= 2
c.) y"+14y'+49y=0, y(0)= -1 and y'(0)= 9
2. Find a two-parameter family of solutions to the following
differential equations
a.) y"-3y'-10y=14e^-2x
b.) y"-6y'+25y=0
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...