## Laplace Question

Limits, differentiation, related rates, integration, trig integrals, etc.
acer400
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Joined: Thu Dec 15, 2011 5:44 pm
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### Laplace Question

So the question is: A curve rise from the origin of the xy plane into the 1st quadrant. The area under the curve from (0,0) to (x,y) is 1/5 the area of the rectangle with these points as opposite vertices.

So i'm solving for f(x):
So far what i have is:

Area(D)=1/5 xy=integral 0 to x y(t)dt
and then

rewrite as: 1/5xy = integral 0 to x g(x-t)y(t) dt, where g(t)=1

then the next step i get stuck, because when i take the Laplace of both sides i get: 1/5L[xy]=L[y]

Thanks in advance for any help.

nona.m.nona
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Joined: Sun Dec 14, 2008 11:07 pm
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### Re: Laplace Question

Is it necessary to use Laplace transforms, rather than any other method?

Thank you.

acer400
Posts: 2
Joined: Thu Dec 15, 2011 5:44 pm
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### Re: Laplace Question

I think i just need to use laplace to get to the current step and solve using ODE after that, but i am unsure if that is correct?

nona.m.nona
Posts: 288
Joined: Sun Dec 14, 2008 11:07 pm
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### Re: Laplace Question

I could be incorrect, but it seems to me that other methods are available. In very crude terms, perhaps the following is useful:

$\frac{1}{5}xy\, =\, \int\, y\, dx$

$\frac{1}{5}y\, +\, \frac{1}{5}x\frac{dy}{dx}\, =\, y$

$\frac{1}{5}x\frac{dy}{dx}\, =\, \frac{4}{5}y$

$\frac{dy}{y}\, =\, 4\left( \frac{dx}{x}\right)$

$\int\, \frac{1}{y}\, dy\, =\, 4\, \int\, \frac{1}{x}\, dx$