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
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)
Bringing like on the same side we get,
Integrating on both sides we get,
(∵ logC is an arbitrary constant)
Applying exponential on both sides we get,
Cross multiplying on both sides we get,
∴ The solution for the given differential equation is x4 – 2x2y2 = C4.