# In the following example verify that the given expression is a solution of the corresponding differential equation: xy = log y +c; dydxyxydydx=y21-xy - Mathematics and Statistics

Sum

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

xy = log y +c; "dy"/"dx" = "y"^2/(1 - "xy")

#### Solution

xy = log y +c

Differentiating w.r.t. x, we get

"x" * "dy"/"dx" + "y" xx 1 = 1/"y" * "dy"/"dx" + 0

∴ "x" "dy"/"dx" + "y" = 1/"y" * "dy"/"dx"

("x" - 1/"y")"dy"/"dx" = - "y"

∴ (("xy" - 1)/"y") "dy"/"dx" = - "y"

∴ "dy"/"dx" = (- "y"^2)/("xy" - 1) = "y"^2/(1 - "xy"), if xy ≠ 1

Hence, xy = log y + c is a solution of the D.E.

"dy"/"dx" = "y"^2/(1 - "xy"), if xy ≠ 1.

Concept: Formation of Differential Equations
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