Q. 22

# Solve the differe

Given,

(tan-1 y – x)dy = (1 + y2)dx Clearly, this is a linear differential equation. Comparing with the standard form A 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 = The solution is given as:  …(1)

Where I = Let tan-1y = u

du = I = Using integration by parts:

I = I = I = the solution is given using equation 1:  OR

Given, …(1)

Clearly, the equation is homogeneous(can be observed directly)

We know that for solving a homogeneous we differential equation,

We take y = vx.

As y = vx

Differentiating both sides w.r.t x we get  equation 1 can be rewritten as-    Integrating both sides we get-      The above equation gives the general solution. For a particular solution, we need to find the value of C.

As given that at x = 0 ,y = 1 C = 0.

Particular solution at x = 0 and x =1 is given by: Rate this question :

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