- #1

- 95

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Example 1:

x(dy/dx) + y = sin(x) / x

becomes

d/dx(xy) = sin(x) / x

Example 2:

e^-x (dy/dx) - y(e^-x) = e^(-4x/3)

becomes

d/dx(y(e^-x)) = e^(-4x/3)

I'm having trouble rationalizing how this step is performed. Thanks for any help!

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- Thread starter Kavorka
- Start date

- #1

- 95

- 0

Example 1:

x(dy/dx) + y = sin(x) / x

becomes

d/dx(xy) = sin(x) / x

Example 2:

e^-x (dy/dx) - y(e^-x) = e^(-4x/3)

becomes

d/dx(y(e^-x)) = e^(-4x/3)

I'm having trouble rationalizing how this step is performed. Thanks for any help!

- #2

Simon Bridge

Science Advisor

Homework Helper

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http://tutorial.math.lamar.edu/Classes/DE/Linear.aspx

... then attempt to use them on your examples and get back to us.

- #3

Mark44

Mentor

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In both examples they are recognizing that the left side is the derivative, with respect to x, of a product. In the first example, the product is xy. In the second, the product is ye

Example 1:

x(dy/dx) + y = sin(x) / x

becomes

d/dx(xy) = sin(x) / x

Example 2:

e^-x (dy/dx) - y(e^-x) = e^(-4x/3)

becomes

d/dx(y(e^-x)) = e^(-4x/3)

I'm having trouble rationalizing how this step is performed. Thanks for any help!

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