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Chapter 8: Q 13-26MP (page 466)

Question: In Problems 25to 28 , find a particular solution satisfying the given conditions.

when x = 2.

Short Answer

Expert verified

The solution of given differential equation is .

Step by step solution

01

Given information.

The differential equation is .

02

Differential equation.

When fand its derivatives are inserted into the equation, a solution is a function y = f(x) that solves the differential equation. The highest order of any derivative of the unknown function appearing in the equation is the order of a differential equation.

03

Find the solution of the given differential equation.

Consider the equation.

Rearrange above equation.

The above equation is in the form of where

The integrating factor is,

The solution of differential equation is,

Solve further,

Substitute 6 for y and 2 for x in Equation (1).

Substitute 1 for c in Equation (1).

Thus, the solution of given differential equation is

.

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By using Laplace transforms, solve the following differential equations subject to the given initial conditions.

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