question on differential equation on variable seperable

Linear equation in two variable

The solution of differential equation xdy-ydx=0 represents

Statement I Order of differential equation of family of parabola whose axis is parallel to y-axis and latusrectum is fixed is 2. Statement II Order of first equation is same as actual number of arbitary constant present in differential equation.

Which of the following statements on ordinary differential equations is/are true ? (i) The number of arbitrary constants is same as the degree of the differential equation. (ii) A linear differential equation can contain products of the dependent variable and its derivatives. (iii) A particular integral cannot contains arbitrary constants. (iv) By putting v=(y)/(x) any homogeneous first order differential equation transforms to variable separable form.

The general solution of a differential equation is y= ae ^(bx+ c) where are arbitrary constants. The order the differential equation is :

Write down the differential equation of a plane progressive wave.

Obtain the differential equation of all circles of radius rdot

From the differential equation of the family of parabolas with focus at the origin and axis of symmetry along the x-axis. Find the order and degree of the differential equation.

Show that the differential equation (y sin^(2)((x)/(y))-x)dy+ydx = 0 is homogeneous differential equation. Also find its general solution.

Show that the differential equation x^(2)(dy)/(dx) = x^(2)+ xy + y^(2) is homogeneous differential equation. Also find its general solution.