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Form the differential equations by elimi...

Form the differential equations by eliminating the arbitrary constants from the following equations :
` 1. (1) xy = Ae^(x) + Be^(-x) + x^(2) (2) y= e^(-x) (A cos 2x + B sin 2x)`

Text Solution

Verified by Experts

The correct Answer is:
`x(d^(2)y)/(dx^(2)) + 2(dy)/(dx) - xy +x^(2) -2=0` (2) `(d^(2)y)/(dx^(2)) +2dy/dx+5y=0`
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Knowledge Check

  • The differential equation obtained by eliminating the arbitrary constants a and b from xy = ae^(x) + be^(-x) is

    A
    ` x(d^(2)y)/(dx^(2)) +2(dy)/(dx) -xy =0`
    B
    ` (d^(2)y)/(dx^(2))+2y(dy)/(dx) -xy =0`
    C
    ` x (d^(2)y)/(dx^(2)) +2 (dy)/(dx)+xy = 0 `
    D
    ` (d^(2)y)/(dx^(2)) +(dy)/(dx) - xy = 0 `

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