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What is an Airy equation?
An Airy equation is an equation in mathematics, the simplest second-order linear differential equation with a turning point.
What are the degrees of differential equation?
The degree of a differential equation is the POWER of the derivative of the highest order. Using f' to denote df/fx, f'' to denote d2f/dx2 (I hate this browser!!!), and so on, an equation of the form (f'')^2 + (f')^3 - x^4 = 17 is of second degree.
How do you find the locus of all points that lie on the graphs of both x plus 2y equals 1 and 2x -y equals 12?
You solve the two equations simultaneously. There are several ways to do it; one method is to solve the first equation for "x", then replace that in the second equation. This will give you a value for "y". After solving for "y", replace that in any of the two original equations, and solve the remaining equation for "x".You solve the two equations simultaneously. There are several ways to do it; one method is to solve the first equation for "x", then replace that in the second equation. This will give you a value for "y". After solving for "y", replace that in any of the two original equations, and solve the remaining equation for "x".You solve the two equations simultaneously. There are several ways to do it; one method is to solve the first equation for "x", then replace that in the second equation. This will give you a value for "y". After solving for "y", replace that in any of the two original equations, and solve the remaining equation for "x".You solve the two equations simultaneously. There are several ways to do it; one method is to solve the first equation for "x", then replace that in the second equation. This will give you a value for "y". After solving for "y", replace that in any of the two original equations, and solve the remaining equation for "x".
What is the name of a second degree equation?
the name is squared equation
What do you do if the second difference in a quadratic equation is 1?
The second difference of a quadratic equation being one indicates the second derivative at that point is positive. What you do from there depends on what property or transformation you're looking for with respect to the equation.
Why euler method for solving first and second order differential equation is not preferred when compared with rungeekutta method?
"http://wiki.answers.com/Q/Why_euler_method_for_solving_first_and_second_order_differential_equation_is_not_preferred_when_compared_with_rungeekutta_method"
What is an Airy equation?
An Airy equation is an equation in mathematics, the simplest second-order linear differential equation with a turning point.
What is second order differential equation?
The highest order of derivative is 2. There will be a second derivative {f''(x) or d2y/dx} in the equation.
What is the Order of a differential equation?
The order of a differential equation is a highest order of derivative in a differential equation. For example, let us assume a differential expression like this. d2y/dx2 + (dy/dx)3 + 8 = 0 In this differential equation, we are seeing highest derivative (d2y/dx2) and also seeing the highest power i.e 3 but it is power of lower derivative dy/dx. According to the definition of differential equation, we should not consider highest power as order but should consider the highest derivative's power i.e 2 as order of the differential equation. Therefore, the order of the differential equation is second order.
What does the second order differential equation represent graphically?
actually it represents the concavity or convexity of a curve
What are the degrees of differential equation?
The degree of a differential equation is the POWER of the derivative of the highest order. Using f' to denote df/fx, f'' to denote d2f/dx2 (I hate this browser!!!), and so on, an equation of the form (f'')^2 + (f')^3 - x^4 = 17 is of second degree.
Main points of Legendre differential equation?
The Legendre differential equation is the second-order ordinary differential equation(1)which can be rewritten(2)The above form is a special case of the so-called "associated Legendre differential equation" corresponding to the case . The Legendre differential equation has regular singular points at , 1, and .If the variable is replaced by , then the Legendre differential equation becomes(3)derived below for the associated () case.Since the Legendre differential equation is a second-order ordinary differential equation, it has two linearly independent solutions. A solution which is regular at finite points is called a Legendre function of the first kind, while a solution which is singular at is called a Legendre function of the second kind. If is an integer, the function of the first kind reduces to a polynomial known as theLegendre polynomial.The Legendre differential equation can be solved using the Frobenius method by making a series expansion with ,(4)(5)(6)Plugging in,(7)(8)(9)(10)(11)(12)(13)(14)so each term must vanish and(15)(16)(17)Therefore,(18)(19)(20)(21)(22)so the even solution is(23)Similarly, the odd solution is(24)If is an even integer, the series reduces to a polynomial of degree with only even powers of and the series diverges. If is an odd integer, the series reduces to a polynomial of degree with only odd powers of and the series diverges. The general solution for an integer is then given by the Legendre polynomials(25)(26)where is chosen so as to yield the normalization and is ahypergeometric function.The associated Legendre differential equation is(27)which can be written(28)(Abramowitz and Stegun 1972; Zwillinger 1997, p. 124). The solutions to this equation are called the associated Legendre polynomials (if is an integer), or associated Legendre functions of the first kind (if is not an integer). The complete solution is(29)where is a Legendre function of the second kind.The associated Legendre differential equation is often written in a form obtained by setting . Plugging the identities(30)(31)(32)(33)into (◇) then gives(34)(35)
What is parabolic heat equation?
The parabolic heat equation is a type of partial differential equation that describes how a quantity, such as temperature, changes in both space and time. It is typically used to model heat diffusion in a given domain with specified boundary and initial conditions. The equation is of second order in time and usually involves first or second order spatial derivatives.
How do you find the locus of all points that lie on the graphs of both x plus 2y equals 1 and 2x -y equals 12?
You solve the two equations simultaneously. There are several ways to do it; one method is to solve the first equation for "x", then replace that in the second equation. This will give you a value for "y". After solving for "y", replace that in any of the two original equations, and solve the remaining equation for "x".You solve the two equations simultaneously. There are several ways to do it; one method is to solve the first equation for "x", then replace that in the second equation. This will give you a value for "y". After solving for "y", replace that in any of the two original equations, and solve the remaining equation for "x".You solve the two equations simultaneously. There are several ways to do it; one method is to solve the first equation for "x", then replace that in the second equation. This will give you a value for "y". After solving for "y", replace that in any of the two original equations, and solve the remaining equation for "x".You solve the two equations simultaneously. There are several ways to do it; one method is to solve the first equation for "x", then replace that in the second equation. This will give you a value for "y". After solving for "y", replace that in any of the two original equations, and solve the remaining equation for "x".
Why sine and cosine are functions of harmonic motion?
Simple harmonic motion (SHM( is defined by the second order differential equation: d2y/dt2 = -ky where y is a fubction of time, t and is the displacement (relative to the central position), and k is a positive constant. The equation says is that at any given position of the object undergoing SHM, its acceleration is proportional to its displacement from, and directed towards the central position. The sine and cosine functions are solutions to the differential equation.
What is quasigeostrophic vertical velocity?
Quasi-geostropic vertical velocity is a unified equation for the vertical velocity of fluid parcels. This equation involves a system of two coupled differential equations. The first is a vorticity equation which comes from the dynamics of uniformly rotating flows. The second is one that depends on the distinctive properties of the considered fluid.
Describe the solution to the system of equations 5x - y equals 8 and 25x-5y equals 32?
Substitution method: from first equation y = 5x - 8. In the second equation this gives 25x - 5(5x - 8) = 32 ie 25x - 25x + 40 = 32 ie 40 = 32 which is not possible, so the system has no solution. Multiplication method: first equation times 5 gives 25x - 5y = 40, but second equation gives 32 as the value of the identical expression. No solution.
