anonymous
  • anonymous
Second order differential equations: 100(y'')-20(y)+y=0. Find general solution. Please explain how to obtain the general solution.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
PLEASE EXPLAIN STEPWISE!!
anonymous
  • anonymous
isnt it 100 y'' -20 y' + y = 0
anonymous
  • anonymous
oops yes

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anonymous
  • anonymous
ok you want a characteristic equation 100 r^2 - 20r + 1 = 0
anonymous
  • anonymous
then?
anonymous
  • anonymous
you have a double root, r = 1/10
anonymous
  • anonymous
ya...then?
anonymous
  • anonymous
If tex2html_wrap_inline96 (which happens if tex2html_wrap_inline98 ), then the general solution is displaymath64
anonymous
  • anonymous
http://www.sosmath.com/diffeq/second/constantcof/constantcof.html
anonymous
  • anonymous
the general solution is y = c1 *e^(1/10 x) + c2 *x *e^(1/10 x)
anonymous
  • anonymous
is there a way to obtain without memorizing the formula?
anonymous
  • anonymous
not that i know of
anonymous
  • anonymous
there are 3 cases, distinct roots, double roots, and the imaginary roots. its not too bad, there is pattern
anonymous
  • anonymous
the imaginary case is a little tricky
anonymous
  • anonymous
thank you
anonymous
  • anonymous
Can this method also solve differential equations of the form y"=f(x)?
anonymous
  • anonymous
how will u proceed after u take y''=f(x)?
anonymous
  • anonymous
yes it usually makes it easier to reduce the quadratic, except in the case where there are radical linear factors
anonymous
  • anonymous
show that the defferential equation y(y^2+2x)+2x(y^2+x)dy/dx=0 is not exact, but that it has an integrating factor of the form u=x^2y^k for some integer k. hence or otherwise find the general solution of this differential equation

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