Solve the IVP: y − 2y + 17y = 0
Question # 00227943
Posted By:
Updated on: 03/21/2016 08:23 AM Due on: 04/20/2016
Practice Midterm II
1. Solve the IVP: y − 2y + 17y = 0;
y(π/4) = 1;
y (π/4) = −1
2. Determine the homogenous O.D.E whose general solution is
y(x) = c1 ex + c2 e−x + c3 xe−x + e−x (A cos(x) + B sin(x))
3. A mass weighing 8 lb stretches a spring 2 ft. Assume there is no damping or external forces acting on
the system. Suppose the mass is pulled down 1 ft below its equilibrium position, and released with an
upward velocity of 4 ft/s.
(a) Determine the position y(t) of the mass at any time t.
(b) Find the amplitude, phase angle and period of the motion.
4. Consider the equation y − 2y + 2y = tet + et sin(t)
(a) Find the solution to the corresponding homogenous equation
(b) Using the Method of Undertermined Coefficients (a.k.a the lucky guess), write down a particular
solution. Do NOT evaluate the coefficients.
5. (a) Verify that y1 (t) = t solves the equation (for t > 0): t2 y + ty − y = 0. Find a second linearly
independent solution using Reduction of Order
(b) Let f (t) = t3 e3t . Find a particular solution to the equation t2 y + ty − y = f (t).
6. Find the general solution to the following homogenous problem: y (5) − 4y (4) + 4y (3) = 0
(Note that y (3) refers to the third derivative and so on...)
7. Using any method you like, find a particular solution to y + 16y = cos4 (x)
(Hint: It is possible to guess a solution here but it is helpful to use some trig identities first)
1
1. Solve the IVP: y − 2y + 17y = 0;
y(π/4) = 1;
y (π/4) = −1
2. Determine the homogenous O.D.E whose general solution is
y(x) = c1 ex + c2 e−x + c3 xe−x + e−x (A cos(x) + B sin(x))
3. A mass weighing 8 lb stretches a spring 2 ft. Assume there is no damping or external forces acting on
the system. Suppose the mass is pulled down 1 ft below its equilibrium position, and released with an
upward velocity of 4 ft/s.
(a) Determine the position y(t) of the mass at any time t.
(b) Find the amplitude, phase angle and period of the motion.
4. Consider the equation y − 2y + 2y = tet + et sin(t)
(a) Find the solution to the corresponding homogenous equation
(b) Using the Method of Undertermined Coefficients (a.k.a the lucky guess), write down a particular
solution. Do NOT evaluate the coefficients.
5. (a) Verify that y1 (t) = t solves the equation (for t > 0): t2 y + ty − y = 0. Find a second linearly
independent solution using Reduction of Order
(b) Let f (t) = t3 e3t . Find a particular solution to the equation t2 y + ty − y = f (t).
6. Find the general solution to the following homogenous problem: y (5) − 4y (4) + 4y (3) = 0
(Note that y (3) refers to the third derivative and so on...)
7. Using any method you like, find a particular solution to y + 16y = cos4 (x)
(Hint: It is possible to guess a solution here but it is helpful to use some trig identities first)
1
-
Rating:
5/
Solution: Solve the IVP: y − 2y + 17y = 0