Questions from General Calculus

Q: (a). Solve the differential equation y' = 2x√1

(a). Solve the differential equation y' = 2x√1 – y2. (b). Solve the initial-value problem y' = 2x√1 – y2, y (0) = 0, and graph the solution. (c). Does the initial-value problem y' = 2x√1 – y2, y (0) =...

Q: (a). Use Euler’s method with step size 0.2

(a). Use Euler’s method with step size 0.2 to estimate y (0.4), where y (x) is the solution of the initial-value problem y' = x + y2, y (0) = 0. (b). Repeat part (a) with step size 0.1.

Q: (a). Program a calculator or computer to use Euler’s method

(a). Program a calculator or computer to use Euler’s method to compute y (1), where y (x) is the solution of the initial value problem (b). Verify that y = 2 + e-x3 is the exact s...

Q: (a). Program your computer algebra system, using Euler’s method

(a). Program your computer algebra system, using Euler’s method with step size 0.01, to calculate y (2), where y is the solution of the initial-value problem (b). Check your work b...

Q: (a). Use a computer algebra system to draw a direction

(a). Use a computer algebra system to draw a direction field for the differential equation. Get a printout and use it to sketch some solution curves without solving the differential equation. (b). Sol...

Q: In Exercise 14 in Section 7.1 we considered a 950C

In Exercise 14 in Section 7.1 we considered a 950C cup of coffee in a 200C room. Suppose it is known that the coffee cools at a rate of 10C per minute when its temperature is 700C. (a). What does the...

Q: Find the orthogonal trajectories of the family of curves. Use a

Find the orthogonal trajectories of the family of curves. Use a graphing device to draw several members of each family on a common screen.

Q: A fish farmer has 5000 catfish in his pond. The number

A fish farmer has 5000 catfish in his pond. The number of catfish increases by 8% per month and the farmer harvests 300 catfish per month. (a). Show that the catfish population Pn after n months is gi...

Q: Find the orthogonal trajectories of the family of curves. Use a

Find the orthogonal trajectories of the family of curves. Use a graphing device to draw several members of each family on a common screen.

Q: Find the orthogonal trajectories of the family of curves. Use a

Find the orthogonal trajectories of the family of curves. Use a graphing device to draw several members of each family on a common screen. y = k/x