Find a general solution of y" + 4y = 0.

Mathematics

1 answer:

klio [65]4 years ago

8 0

Answer:

$y(x)=C_{1}cos2x+C_{2}sin(2x)$

Step-by-step explanation:

It is a linear homogeneous differential equation with constant coefficients:

y" + 4y = 0

Its characteristic equation:

r^2+4=0

r1=2i

r2=-2i

We use these roots in order to find the general solution:

$y(x)=C_{1}cos2x+C_{2}sin(2x)$

You might be interested in

CONDITIONAL PROBABILITY ASSISTANCE

Mars2501 [29]

Consider such events:

A - selected student is freshmen

B - selected student is girl

$A\cap B$ - selected student is freshman is girl

$A|B$ - choosen girl is freshmen.

Use formula $Pr(A|B)=\dfrac{Pr(A\cap B)}{Pr(B)}$ .

From the table you can see that girls that are freshmen are 4 from all 30 people, then $Pr(A\cap B)=\dfrac{4}{30}$ . There are 18 girls, then $Pr(B)=\dfrac{18}{30}$ . Substitute into the formula:

$Pr(A|B)=\dfrac{\frac{4}{30} }{\frac{18}{30} }=\dfrac{4}{18} =\dfrac{2}{9}$ .

Answer: $Pr(A|B)=\dfrac{2}{9}$ .

4 0

4 years ago

What is a counterexample for "subtraction of whole numbers is commutative" ??

devlian [24]

The commutatice property for addition says a+b=b+a
If it was for subtraction, then it would be a-b=b-a
Take a=7 and b=5
7-5 is not equal to 5-7
2 is not equal to -2
So subtraction is not commutative for whole numbers.

Hope this helps :)

6 0

4 years ago

Given two points what’s the slope intersect form (-3, 7) and (1, -1)

UNO [17]

Change in y over the change in x
-1-7=-8
1- -3=4

-8 divided by 4

Slope=-2

5 0

3 years ago

On Monday, 187 students went on a feldtrip to the zoo.All 4 busses were filled and 7 dtudents in a van.How many student were in

RoseWind [281]

Step-by-step explanation:

7 students were in the van so 187 - 7 = 180. 180 ÷ 4 = 45, there were 45 students on each bus. Not sure if this makes total sense, hope it helps

3 0