# Solve the followi

Given differential equation can be written as:

……(1)

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 one side we get,

We know that:

Integrating on both sides, we get,

log(v2 + 1) = -logx + logC ( LogC is an arbitrary constant)

Since y = vx,

we get

( )

Applying exponential on both sides, we get,

Cross multiplying on both sides we get,

y2 + x2 = Cx

The solution for the given differential equation is y2 + x2 = Cx.

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