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Genrish500 [490]
3 years ago
9

First change to standard form of first order linear differential equation and then by finding the appropriate integrating factor

find a particular solution for the initial value problem:xy' + y = lnx ; y(e)=1
Mathematics
1 answer:
Leokris [45]3 years ago
5 0

Answer:

Step-by-step explanation:

Given is a Differential equation as

xy' + y = lnx ; y(e)=1

To bring it to linear form we can divide the full equation by x

y'+\frac{y}{x} =\frac{ln x}{x}

This is of the form

y'+p(x) *y = q(x)

p(x) = 1/x

So find

e^{\int\limits{\frac{1}{x} } \, dx } = e^{ln x} = x

Solution is

xy = \int  {x*lnx /x } \, dx =xln x -x +C

Use the initial value as y(e) =1

e= eln e -e+C\\C=e

So solution is

xy =xln x -x+e

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