Question

1. The complementary function of (D2 + 169)y = 0 is
a. Acos 12x + Bsin 12x
b. A cos 13x + B sin 13x
C. A cos 15x + B sin 15x
Acos 25x + Bsin 25x
d​

Answer 1

$\underline{\textbf{Given:}}$

$\textsf{Differential equation is}$

$\mathsf{(D^2+169)y=0}$

$\underline{\textbf{To find:}}$

$\textsf{Complementary function of the given D.E}$

$\underline{\textbf{Solution:}}$

$\mathsf{Consider,}$

$\mathsf{(D^2+169)y=0}$

$\textsf{Characteristic equation is}$

$\mathsf{m^2+169=0}$

$\mathsf{m^2=-169}$

$\mathsf{m^2=i^213^2}$

$\mathsf{m^2=(13i)^2}$

$\mathsf{m=\pm\,13i}$

$\therefore\textsf{Roots are imaginary}$

$\textsf{Complementary function is}$

$\mathsf{e^{\alpha\,x}[A\,cos\,\beta\,x+B\,sin\,\beta\,x]}$

$\mathsf{=e^{0\,x}[A\,cos\,13\,x+B\,sin\,13\,x]}$

$\mathsf{=e^{0}[A\,cos\,13\,x+B\,sin\,13\,x]}$

$\mathsf{=e^{0}[A\,cos\,13\,x+B\,sin\,13\,x]}$

$\mathsf{=A\,cos\,13\,x+B\,sin\,13\,x}$

$\underrline{\textbf{Answer:}}$

$\mathsf{Option\;(b)\;is\;correct}$

$\underline{\textbf{Find more:}}$

the particular integral of the differential equation (D2+D+1)y=ex is equal to (A) 1/3 ex (B) 3ex (C) ex (D) none of these​

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