In the following example verify that the given expression is a solution of the corresponding differential equation: y = e-x + Ax + B; exdydxexd2ydx2=1 - Mathematics and Statistics

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Sum

In the following example verify that the given expression is a solution of the corresponding differential equation:

y = e-x + Ax + B; `"e"^"x" ("d"^2"y")/"dx"^2 = 1`

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Solution

y = e-x + Ax + B; 

Differentiating w.r.t. x, we get

`"dy"/"dx" = "e"^-"x" xx (- 1) + "A" xx 1 + 0`

`∴ "dy"/"dx" = "e"^-"x" + "A"`

Differentiating again w.r.t. x, we get

`("d"^2"y")/"dx"^2 = - "e"^-"x" xx (- 1) + 0`

∴ `("d"^2"y")/"dx"^2 = 1/"e"^"x"`

∴ `"e"^"x" ("d"^2"y")/"dx"^2 = 1`

Hence, y = e-x + Ax + B is a solution of the D.E.

`"e"^"x" ("d"^2"y")/"dx"^2 = 1`

Concept: Formation of Differential Equations
  Is there an error in this question or solution?
Chapter 6: Differential Equations - Exercise 6.3 [Page 200]

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