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Obtain the differential equation by eliminating arbitrary constants from the following equations. y = (c1 + c2 x) ex - Mathematics and Statistics

Sum

Obtain the differential equation by eliminating arbitrary constants from the following equations.

y = (c1 + c2 x) ex

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Solution

y = (c1 + c2 x) ex

∴ ye -x = c1 + c2x

Differentiating w.r.t. x, we get

`y (-e^-x) + e ^-x  dy/dx = 0 + c_2`

∴`e^-x(dy/dx - y) = c_2`

Again, differentiating w.r.t. x, we get

 `e^-x((d^2y)/dx^2-dy/dx) - e^-x(dy/dx-y) = 0`

∴`e^-x((d^2y)/dx^2-dy/dx - dy/dx+ y) = 0`

∴`(d^2y)/dx^2 - 2dy/dx + y = 0`

Concept: Formation of Differential Equation by Eliminating Arbitary Constant
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APPEARS IN

Balbharati Mathematics and Statistics 1 (Commerce) 12th Standard HSC Maharashtra State Board
Chapter 8 Differential Equation and Applications
Exercise 8.2 | Q 1.3 | Page 163
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