Answer :

Given Differential equation is:


Homogeneous equation: A equation is said to be homogeneous if f(zx,zy) = znf(x,y) (where n is the order of the homogeneous equation).

Let us assume:

f(zx,zy) = z0f(x,y)

So, given differential equation is a homogeneous differential equation.

We need a substitution to solve this type of linear equation, and the substitution is y = vx.

Let us substitute this in (1)

We know that

Bringing like variables on same side we get,

We know that:

-log(1-v2) = logx + logC

log(1-v2)-1 = log(Cx)

( alogx = logxa)

( loga + logb = logab)

Applying exponential on both sides, we get,

Since y = vx, we get,

Cross multiplying on both sides we get,

x = C(x2 – y2)

The solution for the given Differential equation is x = C(X2-y2)

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