Which one of the following differential equations has a solution given by the function y = 5 sin $(3 x + \frac{π}{3})$

\frac{d y}{d x} - \frac{5}{3} c o s (3 x) = 0

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\frac{d y}{d x} + \frac{5}{3} c o s (3 x) = 0

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\frac{d^{2} y}{d^{2} x} + 9 y = 0

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\frac{d^{2} y}{d^{2} x} - 9 y = 0

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Solution

The correct option is C $\frac{d^{2} y}{d^{2} x} + 9 y = 0$
y = 5sin $[3 x + \frac{π}{3}]$

y = 5 $[s i n 3 x . c o s \frac{π}{3} + c o s 3 x . s i n \frac{π}{3}]$

or y = $(5 c o s \frac{π}{3}) s i n (3 x) + (5 s i n \frac{π}{3}) c o s (3 x)$

y = $C_{1} s i n 3 x + C_{2} c o s 3 x (l e t)$

then $\frac{d y}{d x} = 3 C_{1} c o s 3 x - 3 C_{2} s i n 3 x$

$\frac{d^{2} y}{d x^{2}} = - 9 C_{1} s i n 3 x - 9 C_{2} c o s 3 x$

= -9 $[C_{1} s i n (3 x) + C_{2} c o s 3 x]$

$\frac{d^{2} y}{d x^{2}} = - 9 y \Rightarrow \frac{d^{2} y}{d x^{2}} + 9 y = 0$

Suggest Corrections

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