Q. 54

Mark the correct alternative in each of the following:

The general solution of the differential equation ex dy + (y ex + 2x)dx = 0 is

A. x ey + x2 = C

B. x ey + y2 = C

C. y ex + x2 = C

D. y ey + x2 = C

Answer :

ex dy + (y ex + 2x)dx = 0

We can write above equation as

Divide both sides by ex we get,

Since it is a form of linear differential equation.

Integrating Factor (I.F) = e∫ p dx

I.F = e∫ 1 dx = ex

Solution of differential equation is given by

y.(I.F) = ∫ Q.(I.F) dx + C

y ex + x2 = C = (C)

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