Q. 315.0( 1 Vote )

# Find the equation

Given slope at any point = sum of the abscissa and the product of the abscissa and the ordinate = x + xy

According to question,

We can see that it is a linear differential equation.

Comparing it with

P = – x, Q = x

I.F = e∫Pdx

= e – xdx

=

Solution of the given equation is given by

y × I.F = ∫Q × I.F dx + c

y × = ∫ x × dx + c……(1)

Let I = ∫ x × dx

Let

I = ∫ – dt = –

Now substituting the value of I in equation (1)

y + c

y = – 1 + c……(2)

As the equation passing through (0,1),

1 = – 1 + c× 1

c = 2

Putting the value of c in equation (1)

y = – 1 + 2

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