# In the following example verify that the given expression is a solution of the corresponding differential equation: y = eaxxdydxyyeax;xdydx=ylogy - Mathematics and Statistics

Sum

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

y = "e"^"ax"; "x" "dy"/"dx" = "y" log "y"

#### Solution

y = "e"^"ax"

∴ log y = log "e"^"ax" = ax log e

∴ log y = ax        .....(1) .....[∵ log e = 1]

Differentiating w.r.t. x, we get

1/"y" * "dy"/"dx" = "a" xx 1

∴ "dy"/"dx" = "ay"

∴ "x""dy"/"dx" = ("ax")"y"

∴ "x" "dy"/"dx" = "y" log "y"     ....[By (1)]

Hence,  y = "e"^"ax" is a solution of the D.E. "x" "dy"/"dx" = "y" log "y".

Concept: Formation of Differential Equations
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