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How would you use the technique of differential equation for deriving solution to growth in Solow model?
In a Solow model, a differential equation exists because the optimal growth rate is a difference between two functions, whose optimisation is their derivative set equal to zero. Consider:
Break-even investment is equivalent to the minimal level to maintain the capital-labour ratio:
(n + g + d)k(t)
And actual investment is:
sf(k(t))
The differential solution to this equation describes the optimal outcome. Specifically, we optimise economic growth by choosing the savings versus consumption ratio such that the equation
sf(k(t)) - (n + g + d)k(t)
is optimised. This equation represents the derivative of the capital-labour ratio. Therefore, its optimisation is equivalent to
0 = sf(k(t)) - (n + g + d)k(t)
thus
sf(k(t)) = (n + g + d)k(t)
when k(t) = f(k(t)), then
s = n + g + d
What else can I help you with?
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 the global solution of an ordinary differential equation?
The global solution of an ordinary differential equation (ODE) is a solution of which there are no extensions; i.e. you can't add a solution to the global solution to make it more general, the global solution is as general as it gets.
What is the local solution of an ordinary differential equation?
The local solution of an ordinary differential equation (ODE) is the solution you get at a specific point of the function involved in the differential equation. One can Taylor expand the function at this point, turning non-linear ODEs into linear ones, if needed, to find the behavior of the solution around that one specific point. Of course, a local solution tells you very little about the ODE's global solution, but sometimes you don't want to know that anyways.
What is a numerical solution of a partial differential equation?
Some partial differential equations do not have analytical solutions. These can only be solved numerically.
What is oscillatory solution in differential equations?
It happens when the solution for the equation is periodic and contains oscillatory functions such as cos, sin and their combinations.
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 the global solution of an ordinary differential equation?
The global solution of an ordinary differential equation (ODE) is a solution of which there are no extensions; i.e. you can't add a solution to the global solution to make it more general, the global solution is as general as it gets.
What is monge's Method?
Monge's method, also known as the method of characteristics, is a mathematical technique used to solve certain types of partial differential equations. It involves transforming a partial differential equation into a system of ordinary differential equations by introducing characteristic curves. By solving these ordinary differential equations, one can find a solution to the original partial differential equation.
What is complimentary function?
The complementary function, often denoted in the context of solving differential equations, refers to the general solution of the associated homogeneous equation. It represents the part of the solution that satisfies the differential equation without any external forcing terms. In the context of linear differential equations, the complementary function is typically found by solving the homogeneous part of the equation, which involves determining the roots of the characteristic equation. This solution is then combined with a particular solution to obtain the complete solution to the original non-homogeneous equation.
What is the local solution of an ordinary differential equation?
The local solution of an ordinary differential equation (ODE) is the solution you get at a specific point of the function involved in the differential equation. One can Taylor expand the function at this point, turning non-linear ODEs into linear ones, if needed, to find the behavior of the solution around that one specific point. Of course, a local solution tells you very little about the ODE's global solution, but sometimes you don't want to know that anyways.
What is a numerical solution of a partial differential equation?
Some partial differential equations do not have analytical solutions. These can only be solved numerically.
What is impulsive system in differential equation?
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.
What is oscillatory solution in differential equations?
It happens when the solution for the equation is periodic and contains oscillatory functions such as cos, sin and their combinations.
The solution to the differential equation dydxx2y3 , where y (3) 3 is?
y = 43x3+45‾‾‾‾‾‾‾‾‾‾√4
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.
What is a null solution of a differential equation?
A null solution of a differential equation, often referred to as the trivial solution, is a solution where all dependent variables are equal to zero. In the context of linear differential equations, it represents a particular case where the system exhibits no dynamics or behavior; essentially, it indicates the absence of any influence from external forces or initial conditions. The null solution is important in understanding the stability and behavior of the system, as it serves as a baseline for more complex solutions.
Free download solution differential equation of eight edition?
y=c1e^x + c2e^-x
