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quester [9]
2 years ago
10

Consider the differential equation

Mathematics
2 answers:
Minchanka [31]2 years ago
7 0

Answer: For this problem I used the separation method instead of plugging in each one. I thought this would be easiereasier.to

Step-by-step explanation:

Gennadij [26K]2 years ago
4 0

The first solution is quadratic, so its derivative y' on the left side is linear. But the right side would be a polynomial of degree greater than 1, so this is not the correct choice.

The third solution has a similar issue. The derivative of √(x² + 1) will be another expression involving √(x² + 1) on the left side, yet on the right we have y² = x² + 1, so that the entire right side is a polynomial. But polynomials are free of rational powers, so this solution can't work.

This leaves us with the second choice. Recall that

1 + tan²(x) = sec²(x)

and the derivative of tangent,

(tan(x))' = sec²(x)

Also notice that the ODE contains 1 + y². Now, if y = tan(x³/3 + 2), then

y' = sec²(x³/3 + 2) • x²

and substituting y and y' into the ODE gives

sec²(x³/3 + 2) • x² = x² (1 + tan²(x³/3 + 2))

x² sec²(x³/3 + 2) = x² sec²(x³/3 + 2)

which is an identity.

So the solution is y = tan(x³/3 + 2).

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D

Step-by-step explanation:

2.33 I think

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The Marshall Plan differed from the Molotov Plan because it:<br> Really
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A rectangular poster has an area of 190 inches squared. The height of the poster is one inch less than twice its width. Find the
Annette [7]
Set the height to h, and the width to w.

We know that wh=190 and h=2w-1.

Substituting 2w-1 for h, we have:

w(2w-1)=190

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Probability of a standard six side dice landing on a four in the first three rolls?
Illusion [34]

Answer:

91/216

Step-by-step explanation:

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Alternatively, you can calculate it this way.

The probability of getting a 4 on the first roll is 1/6.

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2 years ago
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