Question

Determine the solution of differential equation y"-4y'+4y=0

Answer 1

SOLUTION

TO DETERMINE

The solution of differential equation

y" - 4y' + 4y = 0

EVALUATION

Here the given differential equation is

y" - 4y' + 4y = 0

Let $\sf{y = {e}^{mx} \: }$ be the trial solution

Then the auxiliary equation is

$\sf{ {m}^{2} - 4m + 4 = 0 }$

$\sf{ \implies \: {(m - 2)}^{2} = 0 }$

$\sf{ \implies \: m = 2 \: ,\: 2 }$

Thus the roots are real and equal

So the required solution is

$\sf{y = (a + bx) \: {e}^{2x} }$

Where a and b are constants

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Answer 2

Step-by-step explanation:

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