Answer :

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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