Can y = ax + be a solution of the following differential equation?

If no, find the solution of the D.E. (*).

OR

Check whether the following differential equation is homogeneous or not

Find the general solution of the differential equation using substitution y=vx.

Given,

If, it should satisfy the above equation

Taking RHS of (*)

= y

= LHS

Hence, is a solution of DE(*)

OR

[1]

Now,

Now, for equation to be homogenous, f(x, y) should be homogenous

i.e.

f (zx, zy) = zⁿf(x, y)

Now,

≠ zⁿf (x, y) for any n

Hence, the given equation is not homogenous

Now, put y = vx

Therefore [1], becomes

Integrating both sides,

Put