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प्रश्न
Obtain the differential equation by eliminating arbitrary constants from the following equations.
y = Ae3x + Be−3x
उत्तर
y = Ae3x + B.e−3x ......(i)
Differentiating w.r.t. x, we get
`dy/dx = 3Ae^(3x) - 3 Be ^(-3x)`
Again, differentiating w.r. t. x, we get
`(d^2y)/dx^2 = 3A d/dxe^(3x) -3Bd/dx(e^(-3x))`
= `3A(3e^(3x)) - 3b(-3e^(-3x))`
=`9Ae^(3x)+9Be^(-3x)`
=`9(Ae^(3x)+Be^(-3x)) = 9y` ......[From(i)]
∴ `(d^2y)/dx^2 = 9y`
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