4. 5. Use the method of Frobenius about the regular singular point x indicial roots and recurrence relation for each root. = 0 to find the 2xy" + y + y = 0 A mass weighing 16 pounds stretches a spring 3 inches. The medium offers a damping force that is numerically equal to 2 times the instantaneous velocity. The mass is released from equilibrium with a downward velocity of 3 inches per second. a. Determine the equation of motion. b. Determine the first time (after t = 0) when the mass first passes through equilibrium. 6. Solve the IVP. y" -8y+15y9te² y(0) = −1, y'(0) = 3 7. Find the general solution of the ODE. x2y" 2y 3x² - 1 = x>0 8. Find the general solution of the ODE. y" +2y' - 24y 12x+9e4x 9. Solve the IVP. y" +12y" +36y' = 0 y(0) = 0, y'(0) = 1, y"(0) = -7 1

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.2: Norms And Distance Functions
Problem 43EQ
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4.
5.
Use the method of Frobenius about the regular singular point x
indicial roots and recurrence relation for each root.
= 0 to find the
2xy" + y + y = 0
A mass weighing 16 pounds stretches a spring 3 inches. The medium offers a
damping force that is numerically equal to 2 times the instantaneous velocity. The
mass is released from equilibrium with a downward velocity of 3 inches per
second.
a.
Determine the equation of motion.
b. Determine the first time (after t = 0) when the mass first passes through
equilibrium.
6.
Solve the IVP.
y" -8y+15y9te²
y(0) = −1, y'(0) = 3
7. Find the general solution of the ODE.
x2y" 2y 3x² - 1
=
x>0
8. Find the general solution of the ODE.
y" +2y' - 24y
12x+9e4x
9.
Solve the IVP.
y" +12y" +36y' = 0
y(0) = 0, y'(0) = 1, y"(0) = -7
1
Transcribed Image Text:4. 5. Use the method of Frobenius about the regular singular point x indicial roots and recurrence relation for each root. = 0 to find the 2xy" + y + y = 0 A mass weighing 16 pounds stretches a spring 3 inches. The medium offers a damping force that is numerically equal to 2 times the instantaneous velocity. The mass is released from equilibrium with a downward velocity of 3 inches per second. a. Determine the equation of motion. b. Determine the first time (after t = 0) when the mass first passes through equilibrium. 6. Solve the IVP. y" -8y+15y9te² y(0) = −1, y'(0) = 3 7. Find the general solution of the ODE. x2y" 2y 3x² - 1 = x>0 8. Find the general solution of the ODE. y" +2y' - 24y 12x+9e4x 9. Solve the IVP. y" +12y" +36y' = 0 y(0) = 0, y'(0) = 1, y"(0) = -7 1
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