Solve y ' ' + 4 y = 0 , y ( 0 ) = 2 , y ' ( 0 ) = 2 The resulting oscillation will have Amplitude: Period: If your solution is A sin(rt)+Bcos(rt). The amplitide is given by √ A 2 + B 2 and the period is given by 2 π r

Step-by-step explanation:

This is a homogeneous linear equation. So, assume a solution will be proportional to:

Now, substitute into the differential equation:

Using the characteristic equation:

Factor out

Where:

Therefore the zeros must come from the polynomial:

Solving for :

These roots give the next solutions:

Where and are arbitrary constants. Now, the general solution is the sum of the previous solutions:

Using Euler's identity:

Redefine:

Since these are arbitrary constants

Now, let's find its derivative in order to find and

Evaluating     :

Evaluating     :

Finally, the solution is given by:

y=−9/2x+10

step-by-step explanation:

let's solve for y.

0−9x−2y=−20

step 1: add 9x to both sides.

−9x−2y+9x=−20+9x

−2y=9x−20

step 2: divide both sides by -2.

−2y

−2

=

9x−20

−2

y=

−9

2

x+10

30 miles

step-by-step explanation:

we know that 60 seconds equals 1 minute and 60 minutes 1 hour

44 ft       60 sec     60 min     158400   ft

  *   *   =

1 sec       1 min       1 hour         hour

we know that there are 5280 ft per mile

158400   ft       1 mile         30 miles

  *   =

1   hour               5280 ft     1 hour

so in 1 hour   it can travel 30 miles