What is the differential equation of the family of circles?
(x2+y2)dxdy−2xy=0.
What is the differential equation for the family of circles with Centres on the x-axis?
The equation of a circle with centre at (h, k) and radius equal to a, is (x – h)2 + (y – k)2 = a2. When the circle passes through the origin and centre lies on x-axis i.e., h = a and k = 0.
What is the differential equation of straight line?
The differential equation of all straight lines which are at a constant distance p from the origin is (y−xy1)2=p2(1+y12)
Which one of the following equations represents the differential equation of circles with Centres on the x-axis and all passing through the origin?
The differential equation of all circles passing through the origin and having their centres on the x-axis is. x2+ y2 + 2gx = 0.
How do you find the solution of a differential equation?
For any given differential equation, the solution is of the form f (x,y,c1,c2, …….,cn) = 0 where x and y are the variables and c1 , c2 ……. cn are the arbitrary constants. To learn the formation of differential equations in a detailed way, you are provided with suitable differential equations examples below with few important steps.
What is the equation of system of circles touching y axis at origin?
Equation of a circle with centre at (a,0) and radius a. (x─a)²+(y─0)² = a². That is, x²+y²─2ax = 0 ─────► (1) The above equation represents the family of circles touching Y axis at origin. Here ‘a’ is an arbitrary constant. In order to find the differential equation of system of circles touching Y axis at origin,
What is the equation for x + y^2 = R^2?
If they all have center at origin then the equation is [math]x^2 + y^2 = r^2 [/math] there are numerous differential equations that can be constructed that has such a solution for x and y. Differentiating it with respect to x gives you [math]2x + 2yy’ = 0 [/math] or [math]y’ = -x/y [/math] for example.