# Find the particul

Given,

(tan-1 y – x)dy = (1 + y2)dx

Clearly this is a linear differential equation. Comparing with the standard form

Solution of such equation is given by:

x(I.F) = where I.F = integrating factor

We get P(y) = & Q(y) =

Integrating factor I.F is given :

I.F =

We know that:

I.F =

Solution is given as:

…(1)

Where I =

Let tan-1y = u

du =

I =

Using integration by parts:

I =

I =

I =

solution is given using equation 1:

…(2)

As we have to find particular solution, so we need to find value of C.

Given: x = 0, y = 0

putting the values in eq (2)

0 = tan-1(0) – 1 +

C = 1

particular solution is –

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