Q. 105.0( 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 x = vy.

Let us substitute this in (1)

We know that:

Bringing like variables on the same side we get,

We know that ∫exdx = ex + C and

Integrating on both sides, we get,

ev = logy + C

Since x = vy, we get

The solution for the given Differential equation is .

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