Question

Help me with first order ordinary differential equation

Answer 1

please can any one explain especially the integration part

Answer 2

yes

Answer 3

i dont have any question at hand so youll have to explain on your own sorry

Answer 4

ok lets take an example

Answer 5

dy/dx = x/y

Answer 6

rearranging the equation we get
ydy = xdx

Answer 7

integrating both the sides we get:
y^2 / 2= x^2 /2 + C

Answer 8

where C is constant of integration

Answer 9

ok but can you explain the ones with trigonometric expression or the one in after integration we get ln and especially properties related to ln

Answer 10

@LilySwan i hope this makes it clear

Answer 11

Get some popcorn, and try Khan's videos
https://www.khanacademy.org/math/differential-equations/first-order-differential-equations/differential-equations-intro/v/differential-equation-introduction

Answer 12

u got a question for this one.

Answer 13

equation 1 is the solution of differential equation, this solution can be obtained using any specific method, that depends on the question.

Answer 14

to give a final solution we need to have boundary conditions.

Answer 15

yep but can you help with finding the value of C1......C3

Answer 16

yeah i can surely

Answer 17

there are three BCs Y(2) = 0 , Y' (2)= 2, Y" (2) =6

Answer 18

now the solution is of the form
y= c1x + c2x2 + c3x3

Answer 19

i am not using the powers but writing it ordinarily.

Answer 20

we've got Y(2) the value of Y at x=2. get an equation in c1,c2,c3

Answer 21

differentiating the solution we get 2c2X+3c3x2 = Y'

Answer 22

similarly Y" = 2c2+6c3x

Answer 23

@LilySwan u getting

Answer 24

ya

Answer 25

so u need to put the particular values of x to get the equations in C1 C2 C3 here in this case 3 constants were there so 3 boundary conditions were required.

Answer 26

i hope this must have cleared u with something. @LilySwan