Find a particular solution Satisfying the given condition Function, y = sin x

Asked by Aaryan | 1 year ago |  69

##### Solution :-

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 ago

### Related Questions

#### Find the particular solution satisfying the given condition (dy/dx) = (x – 1)dy/dx = 2x3y

Find the particular solution satisfying the given condition $$(\dfrac{dy}{dx}) = (x – 1)\dfrac{dy}{dx} = 2x^3y$$

#### If the interest is compounded continuously at 6% per annum, how much worth Rs. 1000 will be after 10 years?

If the interest is compounded continuously at 6% per annum, how much worth Rs. 1000 will be after 10 years? How long will it take to double Rs. 1000?

#### In a culture, the bacteria count is 1,00,000. The number is increased by 10% in 2 hours.

In a culture, the bacteria count is 1,00,000. The number is increased by 10% in 2 hours. In how many hours will the count reach 2,00,000, if the rate of growth of bacteria is proportional to the number present?