The function y = cx is the solution of differential equation dddydx=yx - Mathematics and Statistics

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MCQ
True or False

The function y = cx is the solution of differential equation `("d"y)/("d"x) = y/x`

Options

  • True

  • False

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Solution

This statement is True.

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Chapter 1.8: Differential Equation and Applications - Q.3

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y = `a + b/x`

`(dy)/(dx) = square`

`(d^2y)/(dx^2) = square`

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= `x square + 2 square`

= `square`

Hence y = `a + b/x` is solution of `square`


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`square`

This is the general solution.


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Solution: `("d"y)/("d"x)` = cos(x + y)    ......(1)

Put `square`

∴ `1 + ("d"y)/("d"x) = "dv"/("d"x)`

∴ `("d"y)/("d"x) = "dv"/("d"x) - 1`

∴ (1) becomes `"dv"/("d"x) - 1` = cos v

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∴ `square` dv = dx

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∴ `1/2* (tan("v"/2))/(1/2)` = x + c

∴ `square` = x + c


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Solution: The given D.E. is `("d"y)/("d"x)` = e2y cos x

∴ `1/"e"^(2y)  "d"y` = cos x dx

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This is general solution.

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∴ particular solution is `square`


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