From the question it is given that,

Function, y = sin x … [equation (i)]

Now, differentiate with respect x,

\( \dfrac{ dy}{dx}\) = cos x … [equation (ii)]

Then, the above equation is again differentiating with respect to x we get,

\( \dfrac{ d^2y}{dx^2}\) = – sin x

From equation (i) y = sin x

So,

\( \dfrac{ d^2y}{dx^2}\) = – y

Transposing we get,

\( \dfrac{ d^2y}{dx^2}\) + y = 0

Therefore, y = sin x is a solution of the equation.

Then, substitute x = 0 in equation (i)

So, y = sin (0)

y = 0

Hence, y(0) = 0

Now, substitute x = 0 in equation (ii)

\( \dfrac{ dy}{dx}\)= cos (0)

\( \dfrac{ dy}{dx}\) = 1

Hence, (\( \dfrac{ dy}{dx}\)) (0) = 1

Answered by Aaryan | 1 year agoFind the particular solution satisfying the given condition \( (\dfrac{dy}{dx}) = (x – 1)\dfrac{dy}{dx} = 2x^3y\)

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