- #1

- 2

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Can anyone give some clues on how to solve this differential equation:

f '(x) = 3 * f(x)

Thanks!

f '(x) = 3 * f(x)

Thanks!

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- Thread starter pilmr
- Start date

- #1

- 2

- 0

Can anyone give some clues on how to solve this differential equation:

f '(x) = 3 * f(x)

Thanks!

f '(x) = 3 * f(x)

Thanks!

- #2

- 24

- 0

If the problem is asking to solve for f(x)...

Then, I'd first ask myself, what function is equal to its derivative.

I only know of one function: e^x

Therefore, the answer must be of be form: e^(kx), where k is some constant.

Does that help?

- #3

- 13

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lets say y = f(x) for funsies

y' = 3y

(dy/dx) = 3y

dy/(3y) = dx

Integrate with respect to both sides...

right side = X+ C

Left side, , it equals (1/3)*(lny) (technically absolute value of y, but whatevs)

so

ln(y) = 3x + 3c ... which we can also say 3x + C, since C is an arbitrary constant

ln(y) = 3x+C

y = e^(3x+C)

y = (e^(3x))(e^C)

e^C is a constant, so we can say thats C

so...

y = Ce^(3x)

- #4

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Thank you guys, got it now.

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