Find a particular solution Satisfying the given condition y = A cos x + B sin x

Asked by Aaryan | 1 year ago |  57

##### Solution :-

From the question it is given that,

y = A cos x + B sin x … [equation (i)]

Now, differentiate the equation (i) with respect x,

$$\dfrac{ dy}{dx}$$= – A sin x + B cos x … [equation (ii)]

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

$$\dfrac{ d^2y}{dx^2}$$= – A cos x – B sin x … [equation (iii)]

The given differential equation is $$\dfrac{ d^2y}{dx^2}$$+ y = 0

Substitute the equation (i) and equation (iii) in given differential equation,

(- A cos x – B sin x) + (A cos x + B sin x ) = 0

– A cos x – B sin x + A cos x + B sin x = 0

0 = 0

Hence it is verified that, y = A cos x + B sin x is a solution of the differential equation is $$\dfrac{ d^2y}{dx^2}$$ + y = 0.

Answered by Aaryan | 1 year ago

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