Question

(D^2+1)^2y=0 find the solution of the given differential equation​

Answer 1

Answer:

They are "First Order" when there is only dy dx , not d2y dx2 or d3y dx3 etc ... Step 4: Solve using separation of variables to find u ... They are the solution to the equation dy dx − y x = 1 .

Answer 2

Answer:

y= c₁cosx + c₂sinx

Step-by-step explanation:

Concept= Second order Differential Equation

Given= Differential equation

To find= Solution of Differential Equation

Explanation=

We have been given the differential equation as (D^2+1)^2y=0

This is a second order differential equation as its order is 2.

Here D is the symbolic operator.

We know D is dy/dx

and D^2 is d²y/dx²

so the equations become (d²y/dx² +1)²y=0

so (d²y/dx² +1)²=0

(d²y/dx² +1)=0

Let dy/dx be n and the auxiliary solution be eⁿˣ

so n²+1=0

n= +i,-i  (Imaginary roots)

we know that solution of imaginary roots is written as

cosn + sinn

the solution of differential equation is y= c₁cosx + c₂sinx.

Therefore the solution of given differential equation (D^2+1)^2y=0 is

y= c₁cosx + c₂sinx.

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