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in Differential Equations by (28.7k points)
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Solve the following equations:

yex/y dx = (xex/y + y)dy

1 Answer

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Best answer

Given Differential equation is:

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,

∴ The solution for the given Differential equation is

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