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The function y = ex is solution ______ of differential equation - Mathematics and Statistics

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प्रश्न

The function y = ex is solution  ______ of differential equation

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उत्तर

`("d"y)/("d"x) = y`

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अध्याय 1.8: Differential Equation and Applications - Q.2

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Find the particular solution of the following differential equation

`("d"y)/("d"x)` = e2y cos x, when x = `pi/6`, y = 0.

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

∴ `1/"e"^(2y)  "d"y` = cos x dx

Integrating, we get

`int square  "d"y` = cos x dx

∴ `("e"^(-2y))/(-2)` = sin x + c1

∴ e–2y = – 2sin x – 2c1

∴ `square` = c, where c = – 2c

This is general solution.

When x = `pi/6`, y = 0, we have

`"e"^0 + 2sin  pi/6` = c

∴ c = `square`

∴ particular solution is `square`


Solve the differential equation `"dy"/"dx" + 2xy` = y


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