# Higher Order Linear Differential equations

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```					    Higher Order Linear Differential equations
Higher Order Linear Differential equations

Differentiation is important and interesting part of mathematics. We use
differentiation process for calculating the rate of particular function with respect
to particular variable like f(x) is a function and d/dx(f(x) is a rate of f(x) with
respect to x.

Now we discuss different type of differentiation equations – For understand the
different type of differentiation equation we assume a function y = f(x) and when
we calculate differentiation of f(x) with respect to x, it produces first order
differentiation equation and these type of first order differentiation contains
dy/dx and example of first order differentiation equation are – if y = sin x, then
dy/dx = cos x When we differentiate dy/dx with respect to x, it produces second
order differentiation equation and these type of second order equation contains
d2y/dx2 form like – if y = sin-1 x,
then d2y/dx2 = x/(1-x2)3/2 When we differentiate d2y/dx2 with respect to x, it
produces third order differentiation equation and these type of third order
differentiation equation contains d3y/dx3 form like – if y = log(sin x), then third
order differentiation equation is d3y/dx3 = 2 sin x * cosec3 x Similarly this
process continues to produce n order differentiation equation and these type of
n order differentiation equation contains dny/dxn form and these type of
equations are called as a higher order differential equations.

A linear equation which contains these higher order derivatives are called as a
higher order linear differential equations.For calculating the higher order
differential equations, we use following steps –

Step 1: First of all we assume given function as a variable like y = f(x).

Step 2: After assuming that variable, we differentiate that variable with respect
to any suitable variable like we differentiate y with respect to x, it produces
dy/dx.

Step 3: According to the equation we again differentiate variable with respect to
that particular variable like if we differentiate dy/dx with respect to x again, it
produces (d2y/dx2), which is a second order differentiation equation.

Step 4: According to situation, we continue this differentiation until we get our
required equation.

Step 5: After all differentiate process, we put the values of dy/dx, d2y/dx2,
…………dny/dxn in that equation, which we want to prove. Now we take some
examples of higher order differential equation –
Thank You

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