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Bond [772]
3 years ago
7

Find the general solution of the equation: x dy/dx + y = xe^x

Mathematics
1 answer:
ioda3 years ago
4 0

Step-by-step explanation:

x*(dy/dx) +y = x*(dy/dx) +1*y=x*(dx/dy)+dx/dx*y = (d(xy) /dx)

d(xy) /dx = x^ex<->

d(xy) =xe^x*dx

We integrate both parts with their respective variables.

Integral of d(xy) is xy+c.

Integral of xe^x*dx is equal to xe^x - e^x+c.

We have to integrate by parts:

Integral(x*e^x) = x*e^x - integral((x) 'e^x) = x*e^x - integral(e^x)= x*e^x-e^x.

We have that xy + c = x*e^x - e^x + c1, where c and c1 are non defined real constants.

So we get that xy= x*e^x - e^x + c2, where c2 is a real constant.

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The head of the Westlane Cultural Center wants to get a sense of how quickly pledges from donors arrive at the center. It takes
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Answer:

95.64% probability that pledges are received within 40 days

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

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In this problem, we have that:

\mu = 28, \sigma = 7

What is the probability that pledges are received within 40 days

This is the pvalue of Z when X = 40. So

Z = \frac{X - \mu}{\sigma}

Z = \frac{40 - 28}{7}

Z = 1.71

Z = 1.71 has a pvalue of 0.9564

95.64% probability that pledges are received within 40 days

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