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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

ConceptFormation of Differential Equation by Eliminating Arbitary Constant

#### 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

Is there an error in this question or solution?

#### 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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