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Differential Equations
dy/dx=x^3cosy
Differential Equations
Formulate a one-dimensional model describing the dynamics of phytoplankton growth C(x, t) in a water mass taking into account the following: D , its diffusion coefficient, α its rate of
growth, β its mortality rate due to sinking. Fixing the area of interest as 0 ≤ x ≤1 and the initial concentration of phytoplankton as 20 moles/cm^3, find the concentration distribution of phytoplankton in 0 ≤ x ≤1 at any time t .
growth, β its mortality rate due to sinking. Fixing the area of interest as 0 ≤ x ≤1 and the initial concentration of phytoplankton as 20 moles/cm^3, find the concentration distribution of phytoplankton in 0 ≤ x ≤1 at any time t .
Differential Equations
(x-4y-9)dx+(4x+y-2)dy=0
Differential Equations
dx( y sin2x) = [1+y^2+cos^x]dy
Differential Equations
find a particular solution of y"-y'-6y =e^-x
Differential Equations
solving eq
y^2(x-y)p+x^2(y-x)q-z(x^2+y^2)=0
y^2(x-y)p+x^2(y-x)q-z(x^2+y^2)=0
Differential Equations
A beam of length 10m is supported at its ends and weighs 100kg/m. The ODE governing Cy" = 100{(x^2)/2 - 5x) where C is a constant. Solve this equation to determine the deflection at x=6m , given that y=0 at x=0 and x=10.
Differential Equations
y(2xy+1)dx-xdy=0
Differential Equations
The rate of change of the value of an investment, S, with respect to time, t ≥ 0, is given by dS dt = e(rt/100)(5r), where r is the annual interest rate (assumed constant) and the principal of the investment is S(0) = 500.The rate of change of the value of an investment, S, with respect to time, t ≥ 0, is given by
Differential Equations
1. A ball with mass m kg is thrown upward with initial velocity 20 m/s from the roof of a building 23 m high. Neglect air resistance.
Use g = 9.8 m/s^2. Round your answers to one decimal place.
(a) Find the maximum height above the ground that the ball reaches.
x max = _______ meters (absolute tolerance +/- 0.1)
(b) Assuming that the ball misses the building on the way down, find the time that it hits the ground.
t tend =______ s (absolute tolerance +/- 0.1)
2. Determine whether the equation is exact. If it is exact, find the solution. If it is not exact, enter NS.
(3x+2)+(3y-3) y prime = 0
Do not enter an arbitary constant.
_________ = c, where c is an arbitrary constant.
Use g = 9.8 m/s^2. Round your answers to one decimal place.
(a) Find the maximum height above the ground that the ball reaches.
x max = _______ meters (absolute tolerance +/- 0.1)
(b) Assuming that the ball misses the building on the way down, find the time that it hits the ground.
t tend =______ s (absolute tolerance +/- 0.1)
2. Determine whether the equation is exact. If it is exact, find the solution. If it is not exact, enter NS.
(3x+2)+(3y-3) y prime = 0
Do not enter an arbitary constant.
_________ = c, where c is an arbitrary constant.
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#331389 on Nov 2022
#331389 on Nov 2022