Q. 105.0( 1 Vote )
Solve the following equations:
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,
⇒ ev = logy + C
Since x = vy, we get
∴ The solution for the given Differential equation is .
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