   Chapter 6, Problem 54RE

Chapter
Section
Textbook Problem

Solving a First-Order Linear Differential Equation In Exercises 53-58, find the general solution of the first-order linear differential equation. e x y ' + 4 e x y = 1

To determine

To calculate: General solution of differential equation exy'+4exy=1.

Explanation

Given:

Differential equation:exy'+4exy=1

Formula used:

Integration of ex is given by

enxdx=enxn+C

According to Fundamental Theorem of Calculus

dydx+Py=Q

Integration of this type is given below

y(I.F.)=(Q×(I.F.))dx+C …… (I.F. is integration factor)

So,

I.F.=ePdx

Calculation:

exy'+4exy=1 ……(1)

Equation (1) can be written as

exdydx+4exy=1dydx+4y=1ex

Here P=4 and Q=1ex

Now put value of P in I.F.=ePdx

I

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