Differential Equations

Applications of ordinary differential equations are commonly used in the engineering field. The equation is used to find the relationship between the various parts of a bridge, as seen in the Euler-Bernoulli Beam Theory.

There are 6 triangles in an 8 sided octagon

four

PDE stands for Partial Differential Equation

A functional relation can have two or more independent variables. In order to analyse the behaviour of the dependent variable, it is necessary to calculate how the dependent varies according to either (or both) of the two independent variables. This variation is obtained by partial differentiation.

It is an equation in which one of the terms is the instantaneous rate of change in one variable, with respect to another (ordinary differential equation). Higher order differential equations could contain rates of change in the rates of change (for example, acceleration is the rate of change in the rate of change of displacement with respect to time). There are also partial differential equations in which the rates of change are given in terms of two, or more, variables.

39 = 3 x 13

52 = 2^2 x 13

169 = 13^2

LCM is: 2^2 x 3 x 13^2 = 2028

[1+(y')2]3 = [yy"+1+(y')2]2

yes

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What is integrating factor of linear differential equation? Ans: assume y = y(x) in the given linear ODE. Then, by an integrating factor of this ODE, we mean a function g(x) such that upon multiplying the ODE by g(x), it is transformed into an exact differential of the nform d[f(x)] = 0.

PDEs are used in simulation of real life models like heat flow equation is used for the analysis of temperature distribution in a body, the wave equation for the motion of a waveforms, the flow equation for the fluid flow and Laplace’s equation for an electrostatic potential.

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.

Derviative of function is also important.So it does not guarantee a desired curve,which might have bumps.

Laplace will only generate an exact answer if initial conditions are provided

A differential equation have a solution. It is continuous in the given region, but the solution of the impulsive differential equations have piecewise continuous.

The impulsive differential system have first order discontinuity. This type of problems have more applications in day today life. Impulses are arise more natural in evolution system.

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A non-square matrix cannot be inverted.

The highest order of derivative is 2. There will be a second derivative {f''(x) or d2y/dx} in the equation.

3 over four is all ways proper and 6 over four like that is improper but if you mean 64 over 4 it is also improper just the way it is

You have to isolate your variable to one side of the equation. Add, subtract, multiply, and divide when necessary.

Sometimes you will get an approximate answer. This means you cant show all of the decimals. For exmaple lets say your variables equals 1/3. Well you cant possibly write 3 infinite because 1/3=0.333 (with infinite 3s). So you write approximately equal to 0.333 Also when you have a variable that is equal to pi (3.14159... etc) you cant possibly write the infinite amount of decimals for this so you write 3 or 4 decimals and then make sure you indicate it is approximate and not equal.

all it is is 6x75=450

72

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.

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