anonymous
  • anonymous
Verify that the given functions form a basis for the space of solutions of the given differential equation. y"+y=0, f1(x)=cosx, f2(x)=sinx
Mathematics
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anonymous
  • anonymous
Verify that the given functions form a basis for the space of solutions of the given differential equation. y"+y=0, f1(x)=cosx, f2(x)=sinx
Mathematics
katieb
  • katieb
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anonymous
  • anonymous
first do u know what sin and cos is ?
anonymous
  • anonymous
lol kind of juss started learing it
anonymous
  • anonymous
ok sin is o/h and cos is a/h

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anonymous
  • anonymous
ok thanks
JamesJ
  • JamesJ
Every second order linear homogeneous equation with linear coefficients \[ y'' + ay' + by = 0 \] has a two dimensional solution space. That is, there exist two linearly independent solutions to the equation. If we call them y_1 and y_2, then the general solution of the equation is \[ y = c_1y_1 + c_2y_2 \] Hence, for your problem, it is sufficient to show that 1. cos x and sin x are solutions of the differential equation; and 2. cos x and sin x are linearly independent You can show number 1 by just showing cos x and sin x satisfy the differential equation. Number 2 I leave to you.

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