Find y as a function of x if: x^2y"-3xy'-21y=0 y(1)=-8 y'(1)=8 y= find y as a function of x if: x^2y"-5xy'-4y=0 y(1)=2 y'(1)=-1 y=

1)

2)

Step-by-step explanation:

For both of these questions, we will use the Reduction of Orders rule of the Second Order Differential Equations.

1) where and

Let where v is a function of x. Then,

Insert them into the equation,

Choose which eliminates

Hence,

Let , then

Hence,

⇒ ⇒

Now let's take the integral of both sides and then use logarithm rule,

Thus,

Use initial conditions now,

Then and

Finally,

is general solution.

2) where and

Let's use

So roots are

By applying initial conditions, constants are found as follows,

Hence,

is general solution

answer:

your answer is: c. 196 7/8 in^3.

the answer is: d) o, f, and kr.

atomic radius of bromine (br) is 114 pm.

atomic radius of oxygen (o) is 73 pm.

atomic radius of fluorine (f) is 72 pm.

atomic radius of krypron (kr) is 112 pm.

the atomic radius of a chemical element is a measure of the size of its atom.

the atomic radius varies with increasing atomic number, but usually increases because of increasing of number of electrons.

the atomic radius decreases across the periods because an increasing number of protons, because greater attraction between the protons and electrons.