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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 is the general solution of a differential equation?
It is the solution of a differential equation without there being any restrictions on the variables (No boundary conditions are given). Presence of arbitrary constants indicates a general solution, the number of arbitrary constants depending on the order of the differential equation.
What is a degree in a differential equation?
A degree of a differential equation is the highest power of highest order of a differential term of the equation. For example, 5(d^4 x/dx^4) - (dx/dx)^2 =7 Here 5(d^4x/dx^2) has the highest order and so the degree will be it's power which is 1.
What is differential equation in mathematics?
It is an equation containing differentials or derivatives, there are situations when variables increase or decrease at certain rates. A direct relationshin between the variables can be found if the differential equation can be solved. Solving differential equations involves an integration process:first order dy _____ which introduces one constant arbitrary dx And secnd order which introduces two arbitrary constant arbitraries 2 d y ______ 2 d x dx
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.
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 is the difference between a first order and a second order differential equation?
A first order differential equation involves only the first derivative of the unknown function, while a second order differential equation involves the second derivative as well.
What is Exact ordinary differential equation?
exact differential equation, is a type of differential equation that can be solved directly with out the use of any other special techniques in the subject. A first order differential equation is called exact differential equation ,if it is the result of a simple differentiation. A exact differential equation the general form P(x,y) y'+Q(x,y)=0Differential equation is a mathematical equation. These equation have some fractions and variables with its derivatives.
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 the difference between fuzzy differential equation and ordinary differential equation?
fuzzy differential equation (FDEs) taken account the information about the behavior of a dynamical system which is uncertainty in order to obtain a more realistic and flexible model. So, we have r as the fuzzy number in the equation whereas ordinary differential equations do not have the fuzzy number.
What is the general solution of a differential equation?
It is the solution of a differential equation without there being any restrictions on the variables (No boundary conditions are given). Presence of arbitrary constants indicates a general solution, the number of arbitrary constants depending on the order of the differential equation.
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 a degree in a differential equation?
A degree of a differential equation is the highest power of highest order of a differential term of the equation. For example, 5(d^4 x/dx^4) - (dx/dx)^2 =7 Here 5(d^4x/dx^2) has the highest order and so the degree will be it's power which is 1.
What are the applications of differential equations?
Many real world problems can be represented by first order differential equation. Some applications of differential equation are radio-active decay and carbon dating, population growth and decay, warming/cooling law and draining a tank.
What is impulsive differential equation?
Differential equation is defined in the domain except at few points (may be consider the time domain ti ) may be (finite or countable) in the domain and a function or difference equation is defined at each ti in the domain. So, differential equation with the impulsive effects we call it as impulsive differential equation (IDE). The solutions of the differential equation is continuous in the domain. But the solutions of the IDE are piecewise continuous in the domain. This is due to the nature of impulsive system. Generally IDE have first order discontinuity. There are so many applications for IDE in practical life.
what is differential equation?
Differential equation is defined in the domain except at few points (may be consider the time domain ti ) may be (finite or countable) in the domain and a function or difference equation is defined at each ti in the domain. So, differential equation with the impulsive effects we call it as impulsive differential equation (IDE). The solutions of the differential equation is continuous in the domain. But the solutions of the IDE are piecewise continuous in the domain. This is due to the nature of impulsive system. Generally IDE have first order discontinuity. There are so many applications for IDE in practical life.
What is the difference between a homogeneous and a non-homogeneous differential equation?
a linear first-order differential equation is homogenous if its right hand side is zero & A linear first-order differential equation is non-homogenous if its right hand side is non-zero.
