# In the following example verify that the given expression is a solution of the corresponding differential equation: y = abxxdydxdydxa+bx;xd2ydx2+2dydx=0 - Mathematics and Statistics

Sum

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

y = "a" + "b"/"x"; "x" ("d"^2"y")/"dx"^2 + 2 "dy"/"dx" = 0

#### Solution

y = "a" + "b"/"x"

Differentiating w.r.t. x, we get

"dy"/"dx" = 0 + "b"(- 1/"x"^2) = - "b"/"x"^2

∴ "x"^2 "dy"/"dx" = - "b"

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

"x"^2 * "d"/"dx" ("dy"/"dx") + "dy"/"dx" * "d"/"dx" ("x"^2) = 0

∴ "x"^2 ("d"^2"y")/"dx"^2 + "dy"/"dx" xx "2x" = 0

∴ "x" ("d"^2"y")/"dx"^2 + 2 "dy"/"dx" = 0

Hence, y = "a" + "b"/"x" is a solution of the D.E.

"x" ("d"^2"y")/"dx"^2 + 2 "dy"/"dx" = 0

Concept: Formation of Differential Equations
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