Differential Eq...

$$x^{\frac{b-c}{bc}} . x^{\frac{c-a}{ca}} . x^{\frac{a-b}{ac}}=$$

The number of arbitrary constants in the particular solution of a differential equation of third order are:

Check whether the function is homogenous or not. If yes then find the degree of the function
$$g(x)=8x^4$$.

What is the solution of the differential equation $$\dfrac {dx}{dy} + \dfrac {x}{y} - y^{2} = 0$$?
where $$c$$ is an arbitrary constant.

What is the solution of the differential equation $$\dfrac {ydx - xdy}{y^{2}} = 0$$?
where $$c$$ is an arbitrary constant.

What is the solution of the differential equation $$\sin \left (\dfrac {dy}{dx}\right ) - a = 0$$?
where $$c$$ is an arbitrary constant.

Check whether the function is homogenous or not. If yes then find the degree of the function
$$g(x)=4-x^2$$.

Which of the following is true regarding the function $$f(x, y)= x^4 \sin \dfrac{x}{y}$$ ?

What is the solution of the differential equation $$\dfrac{dy}{dx} +\dfrac{y}{x} = 0 $$ ?
Where c is a constant.

Find the value of $$k$$ for the function: $$2x^2y+3xyz+z^k$$ to be homogenous.