Q. 85.0( 1 Vote )

# Solve the following equations:

Given Differential equation is:

……(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 same side we get,

We know that:

and

Also,

Integrating on both sides, we get,

( log C is an arbitrary constant)

( alogx = logxa)

( loga + logb = logab)

Since y = vx,

we get,

Applying exponential on both sides we get,

The solution of the Differential equation is

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