Question

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

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Answer 1

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 .

Answer 2

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 : .

 

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

Solution :

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