Differential Equations Answers

1:1

The function g (t) is used to describe the amount g mg of a medical preparation in a body such hours after medication.
a) What does the term g (3)?
b) What do you answer by solving the equation g (t) = 0?
c) For a limited time describes the amount of medicine of the function g (t) = t ^ 2 - 16t + 64th As medicine has disappeared from the body?
d) What are the limitations in time for formula's validity?

Jamal has been an idea for a new computer game that they want to develop. The function T (x) = 100-20x + 2 x → 2 discloses the time in days it takes for the x programmers to develop the game.
a) How many programmers should be set aside for uppgigten if you want the game finished in the shortest possible time?
b) How many days are needed to get the game completed in the shortest possible time?

1. The table below gives the depth of water across a river measured at one metre
intervals between banks.
Distance (m) 0 1 2 3 4
Water depth (m) 0.4 0.5 1.6 0.9 0
Use the Trapezium rule to estimate the cross-sectional area of the river.
A river hydrologist estimates that at the place where this cross sectional data was
measured the average speed of water flow is 0.8m/s. Estimate the volume of water
which passes this section of the river in one minute.

a ball is thrown vertically up. its height x, above ground level at time t is given by x = 40t - 5t2 (squared). where x is in metres and time t is in seconds

a) what is the velocity of the ball at time t
b)what is the maximum height reached by the ball?
c)at what time does the ball reach the ground?
d)what estimate is being used for acceleration due to gravity in the original formula?

d^2x/dt^2 - 4dx/dt -5x =te^(2t)cos 3t

A company wants to manufacture an open cylindrical bucket of volume 10 litres (10000 cm3). The plastic used for the base of the bucket costs 0.03 cents per cm2 while the plastic used for the curved side of the bucket costs 0.02 cents per cm2. Find the radius and height of the bucket for which the bucket has minimum cost. What is the minimum cost? Show all the reasoning and evaluate your answers to 2 decimal places.

1) y"+4y=3x+e^2x, y(0)=0, y'(0)=1
2) y" + y' + y = (sin(x))^2, y(0)=1, y'(0)= -9/2
3) y"+ 3y' + 2y = 3e^-x - 10cos3x, y(0)=0, y'(0) = 2

how to solve it using undetermined coefficient for 2nd method... pls help me..

solve DE

2dy/dx+ 6 y/x = 2tan (x^4)

solve DE :-

x( x+y)dy/dx = y( x-y)