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Problem 6

In each of Problems 1 through 8 determine whether the given pair of functions is linearly independent or linearly dependent. f(t)=t,g(t)=t1

Problem 6

In each of Problems 1 through 10 find the general solution of the given differential equation. y6y+9y=0

Problem 6

A mass of 100g stretches a spring 5cm. If the mass is set in motion from its equilibrium position with a downward velocity of 10cm/sec, and if there is no damping, determine the position u of the mass at any time t. When does the mass first return to its equilibrium position?

Problem 6

use Euler’s formula to write the given expression in the form a + ib. π1+2i

Problem 7

Find the general solution of the given differential equation. In Problems 11 and 12g is an arbitrary continuous function. y+4y+4y=t2e2t,t>0

Problem 7

determine the longest interval in which the given initial value problem is certain to have a unique twice differentiable solution. Do not attempt to find the solution. ty+3y=t,y(1)=1,y(1)=2

Problem 7

A mass weighing 3 Ib stretches a spring 3 in. If the mass is pushed upward, contracting the spring a distance of 1 in, and then set in motion with a downward velocity of 2ft sec, and if there is no damping, find the position u of the mass at any time t. Determine the frequency, period, amplitude, and phase of the motion.

Problem 7

In each of Problems 1 through 10 find the general solution of the given differential equation. 4y+17y+4y=0

Problem 7

In each of Problems 1 through 8 determine whether the given pair of functions is linearly independent or linearly dependent. f(t)=3t,g(t)=|t|

Problem 8

In each of Problems 1 through 8 determine whether the given pair of functions is linearly independent or linearly dependent. f(x)=x3,g(x)=|x|3

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