Problem

In Exercises $1-10,$ solve the differential equat…

07:49

Problem 8 Easy Difficulty

In Exercises $1-10,$ solve the differential equation.
$$y^{\prime}=x(1+y)$$

Answer

$y=C e^{\frac{1}{2} x^{2}}-1$

Related Courses

Calculus 2 / BC

Calculus of a Single Variable

Chapter 6

Differential Equations

Section 2

Differential Equations: Growth and Decay

Discussion

You must be signed in to discuss.

Top Calculus 2 / BC Educators

Watch More Solved Questions in Chapter 6

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Problem 11

Problem 12

Problem 13

Problem 14

Problem 15

Problem 16

Problem 17

Problem 18

Problem 19

Problem 20

Problem 21

Problem 22

Problem 23

Problem 24

Problem 25

Problem 26

Problem 27

Problem 28

Problem 29

Problem 30

Problem 31

Problem 32

Problem 33

Problem 34

Problem 35

Problem 36

Problem 37

Problem 38

Problem 39

Problem 40

Problem 41

Problem 42

Problem 43

Problem 44

Problem 45

Problem 46

Problem 47

Problem 48

Problem 49

Problem 50

Problem 51

Problem 52

Problem 53

Problem 54

Problem 55

Problem 56

Problem 57

Problem 58

Problem 59

Problem 60

Problem 61

Problem 62

Problem 63

Problem 64

Problem 65

Problem 66

Problem 67

Problem 68

Problem 69

Problem 70

Problem 71

Problem 72

Problem 73

Problem 74

Problem 75

Problem 76

Problem 77

Problem 78

Video Transcript

Hello. Hello. Hello. Way need to solve this differential equation on the method. Basic myth that we are going to be able to use is the same method as in example one see example well, in which the method that we used was separation. The separation off variable. What is the separation of variables entail? We have an equation. And on one side of the equation, we will have variables. Why functions of why d y? And on the other we will have functions of it on the. And once we have separated the variables, we're going to integrate both sides by the appropriate variable. So the first thing we do is we're going to rewrite. This is d Y by the de y the so d y by the X is equal x multiplied one both. Why, in order to achieve the separation, we're going to multiply with the X and divide. With this print Mhm, we're going to multiply with DX and divide with one plus y. What we will have is d Y over one plus one equals experience. No, we integrate. Bye. Each of the by each of the integration variables. And I'm going to read them some of the rules that we're going to use on the left hand side. We're going to use the rules. Dear View U is equal to alien off the absolute value of you we'll see on the right hand side will be making use of extra para vein the integrated as X to the n plus one over that These Constance, we don't write on both sides of the equation just right. I'll just read them on the right hand side. So this is excellent. First, this is going to be X squared over two, and here we're going to have the U is equal to one plus y. So do you is the same d y. So here we will have the l n off. Why? Ln off one pass y is equal smoke further solving this for why we will apply the financial function e to the power off the left hand side and power of the right hand side since the end. Ln are inverse sanctions here we will have one plus y on here. We'll have e to the power of where the Let's see one. Now we apply it to the M plus in remember, we have some off funds. That means that we have a product off power. Right. This side is going to be written as e to the X squared of the two times E to the C one. This is one place for it. So since this is some sort off a constant, we are going to rename this constant to be seen. Um, we're also going to subtract one from either side, arrive to the final solution that y equals. See Time's E to the where money they were solution. The differential equation given food here in the beginning, I hope helped mhm, but

Get More Help with this Textbook