Question

Find the homogeneous linear differential
equation whose auxiliary equation has roots
1, -1 is​

Answer 1

SOLUTION

TO DETERMINE

The homogeneous linear differential equation whose auxiliary equation has roots 1 , -1

EVALUATION

Here it is given that the auxiliary equation has roots 1 , -1

∴ The auxiliary equation is

$\sf{(m - 1)(m + 1) = 0}$

$\sf{ \implies \: {m}^{2} - 1 = 0 }$

Hence the required homogeneous linear differential equation is

$\sf{ ({D}^{2} - 1)y = 0}$

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