If $b_n= ∫_0^{\frac{π}{2}} \frac{cos^2nx}{sinx }dx, n∈N,$ Then

b 3 – b 2 , b 4 – b 3 , b 5 – b 4 are in an A.P. with a common difference –2

If $$b_n= ∫_0^{\frac{π}{2}} \frac{cos^2nx}{sinx }dx, n∈N,$$ Then}

b 3 – b 2 , b 4 – b 3 , b 5 – b 4 are in an A.P. with a common difference –2

$\frac{1}{b_3-b_2},\frac{1}{b_4-b_3},\frac{1}{b_5-b_4}, \text{ are in an A.P. with common difference 2}$

b 3 – b 2 , b 4 – b 3 , b 5 – b 4 are in a G.P.

$\frac{1}{b_3-b_2},\frac{1}{b_4-b_3},\frac{1}{b_5-b_4}, \text{ are in an A.P. with common difference -2}$

If bn= ∫_0^{π/2} cos^2nx/sinx dx, n∈N, Then

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Types of Differential Equations

There are various types of Differential Equation, such as:

Ordinary Differential Equations:

Ordinary Differential Equations is an equation that indicates the relation of having one independent variable x, and one dependent variable y, along with some of its other derivatives.

$F(\frac{dy}{dt},y,t) = 0$

Partial Differential Equations:

A partial differential equation is a type, in which the equation carries many unknown variables with their partial derivatives.

Linear Differential Equations:

It is the linear polynomial equation in which derivatives of different variables exist. Linear Partial Differential Equation derivatives are partial and function is dependent on the variable.

Homogeneous Differential Equations:

When the degree of f(x,y) and g(x,y) is the same, it is known to be a homogeneous differential equation.

$\frac{dy}{dx} = \frac{a_1x + b_1y + c_1}{a_2x + b_2y + c_2}$

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If \(b_n= ∫_0^{\frac{π}{2}} \frac{cos^2nx}{sinx }dx, n∈N,\) Then

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