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For what values of r does the function y = e^(rx) satisfy the differential equation y'' − 4y' + 2y = 0?

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For what values of r does the function y = erx satisfy the differential equation y''  4y' + 2y = 0?

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asked Feb 22, 2015 in CALCULUS by anonymous

2 Answers

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Step 1:

The function is and differential equation is .

The function is .

Apply first derivative on each side with respect to .

Use the derivative rule of exponential :

Apply second derivative on each side with respect to .

answered Feb 22, 2015 by yamin_math Mentor
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Contd......

Step 2:

The differential equation is .

Consider .

Substitute , and in above expression.

 

Take out the common term in the above equation.

Solve the equation for r.

Formula for solving a quadratic equation image : image.

 image

Therefore, The values of r that satisfy the differential equation are image.

Solution :

image.

answered Feb 22, 2015 by yamin_math Mentor

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