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Differential Equations
A differential equation, unlike other mathematical equations, has one or more of its unknowns undergoing a continual change. These equations mathematically describe the most significant phenomena in the universe, including Newtonian and quantum mechanics, waves and oscillators, biological growth and decay, heat, economics, and general relativity. Please direct all concerns about these intricate and all-encompassing equations here.
500 Questions
Why does charge developed by induction disappear quickly?
Asked by Wiki User
"Charge?"
The field produced by an inductor exists ONLY while the current flow is changing,
What is a pressure differential?
Asked by Wiki User
its pressure between suction and discharge flow...
What is the derivative of cos pi x plus sin pi y all to the 8th power equals 44?
Asked by Wiki User
(cos(pi x) + sin(pi y) )^8 = 44
differentiate both sides with respect to x
8 ( cos(pi x) + sin (pi y ) )^7 d/dx ( cos(pi x) + sin (pi y) = 0
8 ( cos(pi x) + sin (pi y ) )^7 (-sin (pi x) pi + cos (pi y) pi dy/dx ) = 0
8 ( cos(pi x) + sin (pi y ) )^7 (pi cos(pi y) dy/dx - pi sin (pi x) ) = 0
cos(pi y) dy/dx - pi sin(pi x) = 0
cos(pi y) dy/dx = sin(pi x)
dy/dx = sin (pi x) / cos(pi y)
What does it mean when a differential equation is linear?
Asked by Bejuzz
It means that the dependent variable and all its derivatives are multiplied by constants only, not by themselves nor by functions containing the independent variable..
For example, (dy/dx) + xy = 0 is non-linear
but (dy/dx) + y = (x^2)coswx is linear.
(Note that it doesnt matter how the function of the independent variable is)
How do you show that a wave function is a solution to the time- independent Schrodinger equation for a simple harmonic oscillator?
Asked by Wiki User
You should substitute your solution in the equation. If the solution is correct you will receive equality. Otherwise your solution is wrong.
What is the definition of unsquaring a number?
Asked by Wiki User
unsquaring a number is to chage it back
How would you use the technique of differential equation for deriving solution to growth in Solow model?
Asked by Wiki User
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 is the heat loss equation?
Asked by Wiki User
Heat loss due to change in temperature:
Q = mc(T2-T1)
Heat loss due to change in phase:
Q = mL
c and L are constants that are specific to each compound at certain temperatures. For water, we usually take c to be 4186 J/(kg*K).
