Question

Eliminate the arbitrary constants.

Any solutions.

Problem is given by the picture.

Answer 1

is there any choices?

Answer 2

Well, there is no any solution to eliminate those constants. Because both are different

Answer 3

something's off.
it's like the general solution for a second order ode with a repeated root.

Answer 4

well I can't stay up... I'm off to bed.

Answer 5

the book say the answer is y"-2y'+y=0
i do not know how to solve it.

Answer 6

but the problem is to eleminate the arbitrary constants which are c1 and c2.

Answer 7

all u have to do is differentiation :) hope this helps

Answer 8

but how? I am having trouble of iy, i know how to get the derivative but i do not know how to eliminate.

Answer 9

@njwild you keep saying you want to eliminate the arbitrary constants but you said the answer was a differential equation so it makes me think you want to work from y=c1e^x+c2xe^x to get y''-2y'+y=0 .
But if you are looking for the constants than you initial conditions.

Answer 10

but how to solve it by a given problem to get the answer with solution.

Answer 11

can u find the value of y' and y' by differentiation??

Answer 12

after differentiation imqwerty , what is the steps of rliminating or the first to eliminate until last to get the answer

Answer 13

@imqwerty I get the y' and y" but i do not know what is the first to eliminate until last to get the answer.

Answer 14

wait m tellin :)

Answer 15

it would take too long to type btw heres the solution - https://www.youtube.com/watch?v=HIdKpnWb2Ws

Answer 16

nt exactly the same but it may help u

Answer 17

If you are trying to get the differential equation from the solution here is my explanation:
\[y=c_1e^x+c_2xe^{x} \\ \text{ the } x \text{ next to the other } e^x \text{ tells us we have a repeated solution \to the } \\ \text{ I will call it the characteristic equation } \\ \text{ since the solution is } y=c_1e^{1 \cdot x}+c_2 xe^{1 \cdot x} \\ \text{ then the solution to the charateristic equation } is r=1 \\ r-1=0 \\ (r-1)^2=0 \text{ since the solution is repeated } \\ r^2-2r+1=0\]
from here it should be easy to write the differential equation

Answer 18

but to figure out what the constants are
you need conditions such as y(a)=b and y'(c)=d
whatever a,b,c, and d are given as

Answer 19

other than that I have no idea what you mean by eliminate the arbitrary constants

Answer 20

@freckles that's what I had typed earlier because we had to look for the repeated root, but it was getting late and the asker drove me nuts, so I was erasing my posts before I logged off. Users should stop posting generic questions and add more details instead of one liners.

Answer 21

differentiate twice and then eliminate c1 and c2 from three equations.