Find the general solution of the given differential equation. dy/dx + y = e^5x

Solution:

A differential equation is an equation that contains at least one derivative of an unknown function, either an ordinary derivative or a partial derivative.

Given,

The differential equation is dy/dx + y = e^5x

We have to find the general solution of the equation.

Multiplying by e^x on both sides,

e^x(dy/dx) + y(e^x) = e^6x

d(e^xy)/dx = e^6x

On integrating,

e^x(y) = \(\int e^{6x}\, dx\)

e^x(y) = (1/6)e^6x + C

y = (1/6)e^5x + Ce^-x

Therefore, the general solution is y = (1/6)e^5x + Ce^-x

Find the general solution of the given differential equation. dy/dx + y = e^5x

Summary:

The general solution of the given differential equation dy/dx + y = e^5x is y = (1/6)e^5x + Ce^-x.