Differential Equation Homework: Solving with Attempted Solution

[rado5]

Homework Statement

Homework Equations

The Attempt at a Solution

If my solution is right please tell me why I should omit $$2xe^{-x}+0.5e^{2x}$$

 

[vela]

You shouldn't omit the particular solution. The initial conditions apply to the complete solution, not just the homogeneous solution.

 

[rado5]

So the solution of my book is wrong as I expected!

In this case we have
$$c_{1}=4 c_{2}=-4.5 c_{3}=0$$

 

[vela]

They can't all be 0 otherwise you'd have y(0)=1/2.

 

[gomunkul51]

Do you know how to solve ODEs with Laplace Transform? it is perfectly suited for constant coefficient ODEs with starting conditions at x=0.

 

[Je m'appelle]

Do you know how to solve ODEs with Laplace Transform? it is perfectly suited for constant coefficient ODEs with starting conditions at x=0.

This is a very good advice. I'd take it, in case you know Laplace Transforms.

 

[vela]

Really? I wouldn't. I find using Laplace transforms for a problem like this is usually more tedious than solving it using the method of undetermined coefficients.

 

[Coto]

Really? I wouldn't. I find using Laplace transforms for a problem like this is usually more tedious than solving it using the method of undetermined coefficients.

Depends if you want to solve the inverse LT by hand. :)

 

[gomunkul51]

But then you have to find the 3 constants that solve the IVP.
and if you solve by Laplace Transform you will find them along the way.

Nevertheless, both ways are good !
and you better know how to solve if by different methods.

Also learn Lagrange's Variation of Parameters, it's a little longer but it's ingenious ! :)

 

[vela]

But with the Laplace transform, you'll need to do a partial fractions decomposition, so you end up having to solve a system of linear equations anyway.

I agree it's good to know both ways. It's kind of neat to see it all work out with Laplace transforms, but once you do it a few times, the novelty wears off. ;)

 

[rado5]

They can't all be 0 otherwise you'd have y(0)=1/2.

Thank you very much for your kind help. I know Laplace but I have to revise it now.

I actually solved it again and I got the same results:
$$c_{1}=4 c_{2}=-4.5 c_{3}=0$$ I mean again $$c_{3}=0$$

 

[vela]

Obviously, you're doing something wrong. Why don't you post your work so we can see where the problem is?

 

[rado5]

 

[vela]

Oh, you did get the right answer. It's just that your equations ran together, so it looked like you got c₁=4c₂=4.5c₃=0 so that all of the coefficients were 0.

If you're going to use LaTeX for something like that, you should put the equations on separate lines. :)

 

[rado5]

Oh, you did get the right answer. It's just that your equations ran together, so it looked like you got c₁=4c₂=4.5c₃=0 so that all of the coefficients were 0.

If you're going to use LaTeX for something like that, you should put the equations on separate lines. :)

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