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Particular Solution of a Differential Equation

Find dy/dx y...

Question

Find dy/dx
$y = a cos (log x) + b sin (log x)$

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Solution

$\begin{matrix} w e h a v e y = a cos (log x) + b sin (log x) \frac{d y}{d x} = \frac{- a sin (log x)}{x} + \frac{b cos (log x)}{x} ∴ x \frac{d y}{d x} = - a sin (log x) + b cos (log x) . \end{matrix}$

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y = a cos (log x) + b sin (log x)

then prove that

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

y = a cos (log x) - b sin (log x)

, then the value of

x^{2} \frac{d^{2} y}{d x^{2}} + x \frac{d y}{d x} + y

y = a cos (log x) + b sin (log x)

y = a c o s (l o g x) + b s i n (l o g x)

is the solution of

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

y = a cos (log x) + b sin (log x),

Find the value of

x^{2} y_{2} + x y_{1} + y

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