# Solve the IVP: y 00 − 2y 0 + 17y = 0; y(π/4) = 1; y 0 (π/4) = −1

Question

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

**30 %**discount on an order above

**$ 100**

Use the following coupon code:

RESEARCH