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Simple Seperable Variables Question Rate Topic: -----

#1 23 January 2012 - 12:46 AM Tracker 


Quark
Solve the following differential equation by separation of variables:

\frac{xdy}{dx} = 4y

My solution is:

\int \frac{dy}{4y} = \int \frac{dx}{x} \Rightarrow ln{\mid 4y \mid} = ln{\mid x \mid} + c

The book's solution is:

y = cx^4

Can anyone show me how they came up this this solution?

Thank you.
0

#2 23 January 2012 - 03:39 AM DrRocket 


Primate

View PostTracker, on 23 January 2012 - 12:46 AM, said:

Solve the following differential equation by separation of variables:

\frac{xdy}{dx} = 4y

My solution is:

\int \frac{dy}{4y} = \int \frac{dx}{x} \Rightarrow ln{\mid 4y \mid} = ln{\mid x \mid} + c

The book's solution is:

y = cx^4

Can anyone show me how they came up this this solution?

Thank you.


Take the log of both sides of the solution in the book.

You can know the name of a bird in all the languages of the world, but when you're finished, you'll know absolutely nothing whatever about the bird... -- Richard P. Feynman
0

#3 25 January 2012 - 03:49 AM Tracker 


Quark

View PostDrRocket, on 23 January 2012 - 03:39 AM, said:

Take the log of both sides of the solution in the book.


y = cx^4 \Rightarrow ln{y} = ln{cx^4} \rightarrow ln{y} = ln{c} + 4ln{x} \rightarrow ln{y} = 4ln{x} + c

I don't understand how the four gets inside the ln to become ln{4y}

Thank you for the help.

Cheers.
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#4 25 January 2012 - 05:45 AM DrRocket 


Primate
\int \frac{dy}{4y} = \int \frac{dx}{x} \Rightarrow \frac{1}{4} ln{\mid y \mid} = ln{\mid x \mid} + c

You can know the name of a bird in all the languages of the world, but when you're finished, you'll know absolutely nothing whatever about the bird... -- Richard P. Feynman
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