Find the particular solution satisfying the given condition $$\dfrac{dy}{dx} = \dfrac{1-cos2y}{1+cos2y}$$

Asked by Sakshi | 1 year ago |  70

##### Solution :-

We know that, 1 – cos 2y = 2 sin2y and 1 + cos 2y = 2 cos2 y

So,

$$\dfrac{dy}{dx}= \dfrac{(2 sin^2 y)}{(2 cos^2 y)}$$

Also we know that,

$$\dfrac{sin θ}{cos θ} = tan θ$$

By cross multiplication,

$$\dfrac{dy}{tan^2 y} = dx$$

Integrating on both side, we get,

∫cot2 y dy = ∫dx

∫ (cosec2 y – 1) dy = ∫dx

– cot y- y + c = x

c = x + y + cot y

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?