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Ilya [14]
3 years ago
8

Find the particular solution that satifies the differential equation and the initial condition. f"(x) = x2 f'(0) = 8, f(0) = 4

Mathematics
1 answer:
viva [34]3 years ago
5 0

Answer:

f(x) = x^4/12 + 8x + 4

Step-by-step explanation:

f"(x) = x^2

Integrate both sides with respect to x

f'(x) = ∫ x^2 dx

= (x^2+1)/2+1

= (x^3)/3 + C

f(0) = 8

Put X = 0

f'(0) = 0+ C

8 = 0 + C

C= 8

f'(x) = x^3/3 + 8

Integrate f(x) again with respect to x

f(x) = ∫ (x^3 / 3 ) +8 dx

= ∫ x^3 / 3 dx + ∫8dx

= x^(3+1) / 3(3+1) + 8x + D

= x^4/12 + 8x + D

f(0) = 4

Put X = 0

f(0) = 0 + 0 + D

4 = D

Therefore

f(x) = x^4 /12 + 8x + 4

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2 years ago
Which one is this please answer it and get thanks from me if ur right
mote1985 [20]

♡ The Question ♡

- Which of the following is equivalent to the power shown below? 8^4

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☆ The Answer ☆

- Your answer should be C!

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♡ The Explanation/Step-By-Step ♡

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4 0
2 years ago
Students can take MATH 080 between one and four times. The​ student's tuition for MATH 080 is ​$ 548.00 If the tuition is increa
melamori03 [73]
2nd attempt carries a price of 6% extra, so (6/100) * 548 is 32.88, so 548 + 32.88, the price is 580.88.

for the 3rd attempt 6% extra of that, (6/100) * 580.88, is 34.8528, so the price is 615.7328.

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8 0
3 years ago
If M is the midpoint of XY, find the coordinates of X if M(-3, -1) and Y(-8, 6) A. (2.5, -5.5) B. (-5.5, 2.5) C. (0, 0) D. (2, -
nadezda [96]

Answer:

(2, -8)

Step-by-step explanation:

(x, y)=(-3, -1)

(x1+x2)/2=-3,

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-------------------

(x1+x2)/2=-3

(y1+y2)/2=-1

---------------------

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x1=2

----------

y1+6=-2

y1=-8

(2, -8)

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2 years ago
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Klio2033 [76]

Answer:

3) 10

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Step-by-step explanation:


4 0
3 years ago
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