# 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

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

#### 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
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