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Solve the differential equation.$ y' + y = 1 $

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$$y=1+C e^{-x}$$

Calculus 2 / BC

Chapter 9

Differential Equations

Section 5

Linear Equations

Harvey Mudd College

Baylor University

Boston College

Lectures

13:37

A differential equation is a mathematical equation for an unknown function of one or several variables that relates the values of the function itself and its derivatives of various orders. An ordinary differential equation (ODE) is a differential equation containing one or more derivatives of a function and their rates of change with respect to the function itself; it can be used to model a wide variety of phenomena. Differential equations can be used to describe many phenomena in physics, including sound, heat, electrostatics, electrodynamics, fluid dynamics, elasticity, quantum mechanics, and general relativity.

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Solve the differential equ…

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Solve the given differenti…

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the first step to solving a differential equation is to find the integrating factor. So we have aged the integral of p of X dx, which in this case is just one D axe which gives us e to the X When we integrate, the integral of one would be, in this context the variable which is acts. Therefore, we're now multiplying this it back into the original equation. So we end up with each the axe. Do you Why over D backs, Plus why times eat the acts. Like I said, we're multiplying all the factors by this we're sending this equal to eat of the axe. Now we need to solve for y right, cause the question said to solve the equations or our end solution is gonna be why equals something. So in this context, we end up with y equals one because we're dividing each of these terms by eating the X. So we end up with one over here because of the extra. I bet you next is just one plus c and then divided by E to the X, which could also be written a c e to the negative x, the negative power when we're writing it on one line

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