Calc Help: Solving Differential Equation y'' + y' - 6y=0 with e^(rt)

Thread starter parwana
Start date Sep 4, 2004

AI Thread Summary

To solve the differential equation y'' + y' - 6y = 0 using the function y = e^(rt), the first and second derivatives of y must be calculated. The first derivative is y' = re^(rt) and the second derivative is y'' = r^2e^(rt). Substituting these derivatives into the differential equation leads to the characteristic equation r^2 + r - 6 = 0. Factoring this equation reveals the values of r that satisfy the original differential equation are r = 2 and r = -3. The solution to the differential equation is thus expressed in terms of these values of r.

Sep 4, 2004

parwana

Calc Help!

For what values of r does the function y= e^(rt) satisfy the differential equation y'' + y' - 6y=0

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Sep 4, 2004

Tide

Science Advisor

Homework Helper

Find the first derivative of of y(t) and its second derivative then use those values in the differential equation. The rest should be obvious!

Sep 4, 2004

Zurtex

Science Advisor

Homework Helper

Remember that e^(rt) can never equal 0.

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