Maths Help Please :) (1 Viewer)

Lindurr · Apr 10, 2012

find the y value of the point whose value is 7 if the point lies on the curve y=f(x) defined by f'(x) = f(x)

Thanks

deswa1 · Apr 10, 2012

Consider the curve f(x) being the line y=0. Therefore f'(x)=0 and f(x)=0 so this satisfies the conditions. When x=7, y=0, therefore the y value is 0.

Carrotsticks · Apr 10, 2012

deswa1 said:
Consider the curve f(x) being the line y=0. Therefore f'(x)=0 and f(x)=0 so this satisfies the conditions. When x=7, y=0, therefore the y value is 0.

But this is assuming that the line y=0 is the only such curve/line satisfying the Differential Equation f'(x) = f(x).

Let y = f(x) and dy/dx = f'(x):

$\\ \frac{dy}{dx} = y \\\\ $Re-arranging this gives:$ \\\\ \frac{dy}{y} = dx \\\\ $Integrating both sides gives:$ \\\\ \ln(y) = x + k \\\\ \Rightarrow y = e^{x+k} \\\\ $So when $ x = 7 $ , $ y = e^{k+7}$

deswa1 · Apr 10, 2012

Carrotsticks said:
But this is assuming that the line y=0 is the only such curve/line satisfying the Differential Equation f'(x) = f(x).

Let y = f(x) and dy/dx = f'(x):

$\\ \frac{dy}{dx} = y \\\\ $Re-arranging this gives:$ \\\\ \frac{dy}{y} = dx \\\\ $Integrating both sides gives:$ \\\\ \ln(y) = x + k \\\\ \Rightarrow y = e^{x+k} \\\\ $So when $ x = 7 $ , $ y = e^{k+7}$

Didn't think of this. Ignore my original solution.

Maths Help Please :) (1 Viewer)

Lindurr

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deswa1

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Carrotsticks

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deswa1

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