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makvit [3.9K]
3 years ago
8

Verify by substitution that the given function is a solution of the given differential equation.x2y′′ + xy′ −y = ln x, y = x −ln

x
Mathematics
1 answer:
ludmilkaskok [199]3 years ago
4 0

Looks like the differential equation is

x² y'' + x y' - y = ln(x)

and the known solution is

y = x - ln(x)

Take the first derivatives of the solution:

y' = 1 - 1/x

y'' = 1/x²

Substitute y and its derivatives into the DE:

x² (1/x²) + x (1 - 1/x) - (x - ln(x)) = ln(x)

If y is a valid solution, then this equation should reduce to an identity.

1 + x - 1 - x + ln(x) = ln(x)

0 = 0   ✓

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Solve for x and y. 3x+8y=20. 5x+3y=23
GrogVix [38]

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x=4 and y=1

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Equation 1) 3x+8y=20  

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Which of the following expressions has a value of 2/5 in the picture below?
Anuta_ua [19.1K]

Step-by-step explanation:

<u>Step 1:  List out all of the formulas for the trigonometric functions </u>

<em>sin(x) </em>= opposite/hypotenuse

<em>cos(x) </em>= adjacent/hypotenuse

<em>tan(x) </em>= opposite/adjacent

<u>Step 2:  Find the following expression that has a value of 2/5 </u>

sin(B) = opposite/hypotenuse = ?/5 is FALSE

cos(B) = adjacent/hypotenuse = 2/5 is TRUE

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3 years ago
What is the solution to this system of equations? 2t + w = 10 4t = 20 − 2w A. It has no solution. B. It has infinite solutions.
joja [24]

Answer:

<h3>B. It has infinite solutions</h3>

Step-by-step explanation:

Given the system of equations:

2t + w = 10 ..... 1

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From 1:

w = 10-2t ...3

Substitute 3 into 2 to have;

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Let t = k

Substitute t = k into 1 and get w;

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2k + w =10

w = 10 - 2k

<em>k can take any integers. This shows that the solution to the equation is infinite</em>

<em></em>

7 0
3 years ago
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