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# 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 Rate this question :

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