Why Does Substitution Fail in Solving Differential Equations?

[shreddinglicks]

Homework Statement

I want to solve number 13. I have my work on the attached file.

Homework Equations

The Attempt at a Solution

I've tried to solve the system by elimination and substitution. I keep failing again and again

 

[SteamKing]

Homework Statement

I want to solve number 13. I have my work on the attached file.

Homework Equations

The Attempt at a Solution

I've tried to solve the system by elimination and substitution. I keep failing again and again

Great! What's number 13? Your attachment (which is upside down, thank you very much) has several different scribbles at the top of the page, one of which appears to be '11.'

The thread title mentions 'differential equation', but your thread talks about 'elimination and substitution', which doesn't suggest solving a DE.

Care to start over?

 

[Mark44]

Homework Statement

I want to solve number 13. I have my work on the attached file.

Homework Equations

The Attempt at a Solution

I've tried to solve the system by elimination and substitution. I keep failing again and again

Please take the time to post your work right side up. Better yet, type your work here in the input pane as text.

 

[Mark44]

Homework Statement

I want to solve number 13. I have my work on the attached file.

Homework Equations

The Attempt at a Solution

I've tried to solve the system by elimination and substitution. I keep failing again and again

Please take the time to post your work right side up. If you can't be bothered to make it easy to help you, many homework helpers here will choose not to jump in.

Better yet, type your work here in the input pane as text.

 

[shreddinglicks]

I apologize, I posted this in haste and did not check to see if my post was upside down. I do not see how it's illegible. You will see towards the right there is a #13. The problem has two equations that are boxed in with C1 and C2. I need to solve for the two variables. I can't seem to get the correct values of C1 and C2.

y = C1e^x + C2e^x
y' = C1e^x - C2e^-x

y(-1) = 5
y'(-1) = -5

In case it's not legible.

I end up with a systems of equations after I plug in the info I am given. Which I have boxed in on the attachment.

 

[shreddinglicks]

The attachment

 

[Mark44]

I apologize, I posted this in haste and did not check to see if my post was upside down. I do not see how it's illegible. You will see towards the right there is a #13. The problem has two equations that are boxed in with C1 and C2. I need to solve for the two variables. I can't seem to get the correct values of C1 and C2.

y = C1e^x + C2e^x
y' = C1e^x - C2e^-x

Typo in the first equation above. It should be y = C1e^x + C2e^(-x)

y(-1) = 5
y'(-1) = -5

In case it's not legible.

I end up with a systems of equations after I plug in the info I am given. Which I have boxed in on the attachment.

 

[Mark44]

You are substituting incorrectly.
y(-1) = 5 means you should replace x by -1 and y by 5. You are doing the opposite.
Same thing in the 2nd equation.