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Obtain the Differential Equation by Eliminating the Arbitrary Constants from the Following Equation : Y = C 1 E 2 X + C 2 E − 2 X - Mathematics and Statistics

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Question

Obtain the differential equation by eliminating the arbitrary constants from the following equation :

`y = c_1e^(2x) + c_2e^(-2x)`

Solution

`y = c_1e^(2x) + c_2e^(-2x)`

differentiate w.r.t. x.

`(dy)/(dx) = 2c_1e^(2x) - 2c_2e^(-2x)`

Again diff. w.r.t. x.

`(d^2y)/(dx^2) =4c_1e^(2x) + 4c_2e^(-2x)`

`= 4(c_1e^(2x) + c_2e^(-2x))`

= 4y

`:. (d^2y)/(dx^2) - 4y = 0`

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APPEARS IN

 2017-2018 (March) (with solutions)
Question 4.2.4 | 2.00 marks
Solution Obtain the Differential Equation by Eliminating the Arbitrary Constants from the Following Equation : Y = C 1 E 2 X + C 2 E − 2 X Concept: Formation of Differential Equation by Eliminating Arbitary Constant.
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