Question

3. The complementary function of (D2 + 625)y=0 is
a. Acos 12x + Bsin 12x
b. A cos 13x + B sin 13x
C. A cos 15x + B sin 15x
d. Acos 25x + Bsin 25x
with process​

Answer 1

SOLUTION

TO CHOOSE THE CORRECT OPTION

The complementary function of (D² + 625)y=0 is

a. Acos 12x + Bsin 12x

b. A cos 13x + B sin 13x

C. A cos 15x + B sin 15x

d. Acos 25x + Bsin 25x

EVALUATION

Here the given differential equation is

$\sf{( {D}^{2} + 625)y = 0 }$

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

Then auxiliary equation is

$\sf{ {m}^{2} + 625 = 0 }$

$\sf{ \implies \: m = \pm \: 25}$

Hence the required complementary function is

$\sf{y = A \cos 25x + B \sin 25x}$

FINAL ANSWER

Hence the correct option is

$\sf{d. \: \: \: A \cos 25x + B \sin 25x}$

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Answer 2

Answer:

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