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Mrs.Math101

  • 4 years ago

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

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  1. sunsetlove
    • 4 years ago
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    first do u know what sin and cos is ?

  2. Mrs.Math101
    • 4 years ago
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    lol kind of juss started learing it

  3. sunsetlove
    • 4 years ago
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    ok sin is o/h and cos is a/h

  4. Mrs.Math101
    • 4 years ago
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    ok thanks

  5. JamesJ
    • 4 years ago
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    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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