Question

In: Advanced Math

Solve the following initial value problem d2y/dx2−6dy/dx+25y=0,y(0)=0, dy/dx(0)=1.

Solve the following initial value problem

d2y/dx2−6dy/dx+25y=0,y(0)=0, dy/dx(0)=1.

Solutions

Expert Solution

The given Differential Equation is written as follows:

The Auxiliary Equation is:

The roots are given by:

So,

The solution is given by:

(1)

Given:

y = 0 at x = 0

Substituting in (1), we get:

A = 0

So, (1) becomes:

(2)

Differentiating (2), we get:

(3)

Given:

at x = 0

So, (3) becomes:

So,

B = 1/4

Substituting (2), we get:

So,

the solution of the given differential equation is given by:

Colby Messinger answered 1 year ago

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