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Solve the differential equation x^2 y"-xy' +y 0

Answers

Answer 1

Answer:

Answer:

$y(x)\ =\ √(x)[C_1cos(√(3))/(2)logx+C_2sin(√(3))/(2)logx]$

Step-by-step explanation:

Given differential equation is

$x^2y$ (1)

Let's assume that

$x=e^t$

$=>\ t\ =\ logx$

then,

$(dx)/(dt)=e^t$

$and\ (d^2x)/(dt^2)=e^t$

We can write,

$(dy)/(dx)=(dy)/(dt).(dt)/(dx)$

$=e^(-t)(dy)/(dt)$

Similarly,

$(d^2y)/(dt^2)=(d^2y)/(dt^2).(dt^2)/(dx^2)$

$=e^(-2t).(d^2y)/(dt^2)$

Putting these values in equation (1), we will get

$e^(2t).e^(-2t).(d^y)/(dt^2)-e^t.e^(-t)(dy)/(dt)+y=0$

$=>(d^2y)/(dt^2)-(dy)/(dt)+y=0$

So, the characteristics equation can be given as

$D^2-D+1=0$

$=>D\ =\ (1+√(1-4))/(2)\ or\ (1-1√(1-4))/(2)$

$=>D=\ (1)/(2)+i(√(3))/(2)\ or\ (1)/(2)-i(√(3))/(2)$

Hence, the general solution of the equation can be give by

$y(t)\ =\ e^{(t)/(2)}[C_1cos(√(3))/(2)t+C_2sin(√(3))/(2)t]$

Now, by putting the value of t in above solution, we will have

$y(x)\ =\ e^{(1)/(2)logx}[C_1cos(√(3))/(2)logx+C_2sin(√(3))/(2)logx]$

$y(x)=\ √(x)[C_1cos(√(3))/(2)logx+C_2sin(√(3))/(2)logx]$

Hence, the solution of above given differential equation can be given by

$y(x)=\ √(x)[C_1cos(√(3))/(2)logx+C_2sin(√(3))/(2)logx]$

Related Questions

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A given binomial distribution has 10 trials and probability of success p=1/3. Compute the standard deviation and explain your solution
A regular octagon can be concave.True or False? Please explain.Thanks!
Find the probability. One digit from the number 3,151,221 is written on each of seven cards. What is the probability of drawing a card that shows 3, 1, or 5?a. 2/7b. 5/7c. 3/7d. 4/7
A)0.5B)2.5C)-0.5D)-2.5

FACTOR COMPLETELY:
y^3 - 5y^2 - 17y + 21
HINT: one of the factors is (y-1)

Answers

Answer:

Answer:

7,300 meters

Step-by-step explanation:

7.3×1000 = 7300

Step-by-step explanation:

What is the next number in the sequence. 1,121,12321, 1234321

The next number in the sequence is _____

Answers

Answer:

123454321

Step-by-step explanation:

it's a palendrome, made out of a number of numbers in the sqquence.

The population of bacteria M after X minutes is represented by the function M(x)=51(1.03)^x.whqt is the approximate difference between the populations after 3 minutes

Answers

The difference between the populations after 3 minutes is 5.

Population of bacteria

According to the question, the population of bacteria is modeled by the function; $M(x)=51(1.03)^x$ . We have to recall that x refers to the time taken to have an M number of bacteria.

Initially, x = 0 so;

$M(x)=51(1.03)^0$ = 51

After 3 minutes, we have;

$M(x)=51(1.03)^3$ = 56

Difference between the populations after 3 minutes = 56 - 51 = 5

Hence, the difference between the populations after 3 minutes is 5.

Learn more about population of bacteria: brainly.com/question/4332205

Given that m angle KLH=120^ which statement about the must be true? angle HLM is bisected by angle GLJ is bisected by vec LH . m angle KLG=m angle HLJ m angle HLI=m angle LLM

Answers

The true statement is ∠HLM is bisected byLI

What is bisect?

Bisect means to divide a geometric figure to two equal half.
Dividing line is bisector.

Given that ∠KLH=120°

We know that angle of straight line is 180°

∴∠KLM=180°

∠KLH+∠HLM=180°

120°+∠HLM=180°

∠HLM=60°

From figure, ∠HLI=30° and ∠ILM=30°

Line LI cuts the angle HLM into two equal parts such as HLI and ILM.

Therefore, ∠HLM is bisected by LI

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Answer:angle hlm is bisected by Lj

Step-by-step explanation:

A car rental agency advertised renting a car for $24.95 per day and $0.28 per mile. If Greg rents this car for 3 days, how many whole miles can he drive on a $250 budget?miles (Round down to the nearest whole mile.)

Answers

Answer/Step-by-step explanation:

Greg rent the car for 3 day so 3 x 24.95= $74.85 off the top without driving a single mile.

If he has a budget of $250, his remainder budget for mileage is $250 - $74.85 = $175.15.

How many miles he can travel at $0.28/mile with $175.15 budget?

Greg can drive $175.15/0.28 = 625.53 or 625 Miles

im giving my friends 9 cupcakes thats 60 percent of my order how many more cupcakes do i need to get my order to 100 percent

Answers

The number of cupcakes needed to get the order to 100% is 6 cupcakes.

What is a percentage?

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

Example:

50% = 50/100 = 1/2

25% = 25/100 = 1/4

20% = 20/100 = 1/5

10% = 10/100 = 1/10

We have,

60% = 9 cupcakes

Multiply 100/60 on both sides.

100/60 x 60% = 100/60 x 9 cupcakes.

100% = 5 x 3 cupcakes

100% = 15 cupcakes

Thus,

6 morecupcakes are needed.

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Answer:

6 more cupcakes.

Step-by-step explanation:

60% of 15 is 9, so 15-9 is 6.

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