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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