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Why do you need initial condition to solve differential equation?
The solution to a differential equation requires integration. With any integration, there is a constant of integration. This constant can only be found by using additional conditions: initial or boundary.
Application of differential equation in temperature?
Newton's equation of cooling is a differential equation. If K is the temperature of a body at time t, then dK/dt = -r*(K - Kamb) where Kamb is the temperature of the surrounding, and r is a positive constant.
Which constant tells you what the value of maximum and minimum?
Not a constant, but the differential, i.e. gradient, of the equation. It = 0 at maxima and minima, where the curve is at its turning-point(s).
What is the difference between an ordinary differential equation and a partial differential equation?
ordinary differential equation is obtained only one independent variable and partial differential equation is obtained more than one variable.
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
Why do you need initial condition to solve differential equation?
The solution to a differential equation requires integration. With any integration, there is a constant of integration. This constant can only be found by using additional conditions: initial or boundary.
Application of differential equation in temperature?
Newton's equation of cooling is a differential equation. If K is the temperature of a body at time t, then dK/dt = -r*(K - Kamb) where Kamb is the temperature of the surrounding, and r is a positive constant.
Which constant tells you what the value of maximum and minimum?
Not a constant, but the differential, i.e. gradient, of the equation. It = 0 at maxima and minima, where the curve is at its turning-point(s).
What is the difference between an ordinary differential equation and a partial differential equation?
ordinary differential equation is obtained only one independent variable and partial differential equation is obtained more than one variable.
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 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
Application of differential equation in chemistry?
The rate at which a chemical process occurs is usually best described as a differential 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.
The differential equation of the family of straight lines y equals mx is?
The differential equation of the family of straight lines y = mx is given by dy/dx = m. This equation represents that the slope of the line at any point is equal to the constant m. Different values of m will yield different lines within the family.
Example of total partial and original differential equation?
An ordinary differential equation (ODE) has only derivatives of one variable.
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.
Who is father of differential equation?
leibniz
