# Solve the followi

Let us write the given differential equation in the standard form: ……(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 the like variables on one side   We know that: and Integrating on both sides we get  ( logC is also an arbitrary constant) ( )

( xloga = logax)

Applying exponential on both sides, we get, Squaring on both sides we get, Since y = vx

we get    Cross multiplying on both sides we get,

yx2 = c2(y + 2x)

The solution to the given differential equation is yx2 = c2(y + 2x)

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