Question

Find the general solution of y" - 9y' + 20y = 0​

Answer 1

SOLUTION

TO DETERMINE

The general solution of y" - 9y' + 20y = 0

EVALUATION

Here the given differential equation is

y" - 9y' + 20y = 0

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

Then the auxiliary equation is

$\sf{ {m}^{2} - 9m + 20 = 0 }$

$\sf{ \implies \: {m}^{2} - 5m - 4m + 20 = 0 }$

$\sf{ \implies \: (m - 5)(m - 4) = 0 }$

$\sf{ \implies \: m = 5 \:, \: 4 }$

Hence the required solution is

$\sf{y = a \: {e}^{5x} + b \: {e}^{4x} }$

Where a and b are constants

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