Luigi0210
  • Luigi0210
Solve the differential equation:
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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Luigi0210
  • Luigi0210
\[\frac{ d^2y }{ dx^2 }+2\frac{ dy }{ dx }+2y=10\]
anonymous
  • anonymous
Laplace transforms
Jhannybean
  • Jhannybean
\[\large y'' +y'+2y = 10\] how do you do laplace transformations..... :|

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anonymous
  • anonymous
Wait NVM LOL Do you have any initial conditions?
Jhannybean
  • Jhannybean
YEAH got you there. :|
Luigi0210
  • Luigi0210
what's that?
Jhannybean
  • Jhannybean
what's what?
Luigi0210
  • Luigi0210
Laplace transformations..
Jhannybean
  • Jhannybean
Idk....
Luigi0210
  • Luigi0210
or laplace transforms..
reemii
  • reemii
\(y''++y'+2y=10\) 1) Homogeneous equation: \(y''+y+2y=0\) (H) -> \(p(\lambda) = \lambda^2 + \lambda + 2=0\) iff \(\lambda=\frac{-1\pm i\sqrt7}{2} = -\frac12 \pm i\frac{\sqrt7}2\) (i think) The functions \(g(x) = e^{-\frac12x}(A...+B...)\), with \(A,B\in\mathbb R\) are solutions of (H). 2) find a particular solution. It seems that one constant function is solution of this. (\(y(x) = c\) for some \(c\)). 3) write the general form of the solution. This method is quite common.
Jhannybean
  • Jhannybean
@reemii that looks way too complicated...
reemii
  • reemii
it's a method, no need to think. It is likely the asker learned the method. ( @Luigi0210 )
Luigi0210
  • Luigi0210
hm, from what math is it?
reemii
  • reemii
what do you mean?
Luigi0210
  • Luigi0210
Is this method from calculus 2?
reemii
  • reemii
no idea.
reemii
  • reemii
@Loser66 from \(\lambda=-\frac12\pm i \sqrt{7}/2\) you write \(u=-\frac12,v=\sqrt{7}/2\). then (complete version) \(g(x)=e^{ux}(A\cos(vx)+B\sin(vx))\). A solution of the initial equation is \(y(x)=5\). General solution: \(y_\text{gen}(x)=5+g(x)\), \(A,B\in\mathbb R\).
reemii
  • reemii
I'll look into the laplace transorm method. :)
anonymous
  • anonymous
Can't use laplace transforms here without initial conditions. Sry :(
anonymous
  • anonymous
@Loser66 Convert your 2nd order ODE into two 1st order ODE's
Loser66
  • Loser66
@FutureMathProfessor the same with my method.need initial conditions
Loser66
  • Loser66
@FutureMathProfessor You know that I didn't take differential equation yet, how can I know what is Laplace transform? I use my own knowledge only.
anonymous
  • anonymous
@Loser66 This is my DiffEQ test from a VERY similar problem. No initial conditions needed http://gyazo.com/e8615a0188dd35317e433142262c032c.png

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