## How can I get free responses?

The free response of a system is the solution of the describing differential equation of the system, when the input is zero. The easiest way to to this is to integrate the differential equation in Xcos.

### How do you find the volume of a funnel calculus?

To calculate its volume you need to multiply the base area (area of a circle: π * r²) by height and by 1/3: volume = (1/3) * π * r² * h.

How do you find general and particular solutions?

So, to obtain a particular solution, first of all, a general solution is found out and then, by using the given conditions the particular solution is generated. This represents the particular solution of the given equation.

What is a particular solution of a differential equation?

A particular solution of differential equation is a solution of the form y = f(x), which do not have any arbitrary constants. The general solution of the differential equation is of the form y = f(x) or y = ax + b and it has a, b as its arbitrary constants.

## How do you find the radius of a funnel?

The inside of a funnel of height 10 inches has circular cross sections, as shown in the figure above. At height h, the radius of the funnel is given by r = 1/20 (3 + h2), where 0 ≤ h ≤ 10. The units of r and h are inches.

### What is the volume equation of a cone?

V=1/3hπr²
The formula for the volume of a cone is V=1/3hπr².

What is the difference between general solution and particular solution?

The general solution includes all possible solutions and typically includes arbitrary constants (in the case of an ODE) or arbitrary functions (in the case of a PDE.) A solution without arbitrary constants/functions is called a particular solution.

What is the difference between general solution and principal solution?

If the equation involves a variable 0 ≤ x < 2π, then the solutions are called principal solutions. A general solution is one which involves the integer ‘n’ and gives all solutions of a trigonometric equation.