Mathematics, 06.06.2020 16:57 queenskyyt
Verify by substitution that each given function is a solution of the given differential equation.
Primes denote derivatives with respect to x.
1) y'' = 9y ; y1 = e3x , y2 = e-3x
2) y'' - 2y' +2y = 0; y1 = excosx , y2 = exsinx
3) x2y'' + xy' - y = ln x; y1 = x - ln x , y2 = (1/x) - ln xSubstitute y=erx into the given differential equation to determine all values of the constant r for whichy=erx is a solution of the equation.4) 3y''+3y'-4y=0First verify that y(x) satisfies the given differential equation. Then determine a value of the constant C so that y(x) satisfies the given initial condition.
5) y' = y + 1; y(x) = Cex - 1, y(0) = 5
6) xy' - 3y = x3 ; y(x) = x3(C + ln x), y(1) = 17Write a differential equation of the form dy/dx = f(x, y) having the function g as its solution.
7) The line tangent to the graph of g at the point (x, y) intersects the x-axis at the point (x/2 , 0).
8) The time rate of change of a population P is proportional to the square root of P.
9) In a city having a fixed population of P persons, the time rate of change of the number N of those persons who have heard a certain rumor is proportional to the number of those who have not yet heard the rumor.
10) Suppose a population P of rodents satisfies the differential equation dP/dt = kP2. Initially, there are P(0) = 2 rodents, and their number is increasing at the rate of dP/dt = 1 rodent per month when there are P = 10 rodents. How long will it take for this population to grow to a hundred rodents? To a thousand? What's happening here?
Answers: 3
Mathematics, 21.06.2019 19:00
What is the expression in factored form? -20x^2 - 12x a. 4x(5x+3) b. -4x(5x-3) c. -4(5x+3) d. -4x(5x+3)
Answers: 2
Mathematics, 22.06.2019 02:00
Pleasseee important quick note: enter your answer and show all the steps that you use to solve this problem in the space provided. use the circle graph shown below to answer the question. a pie chart labeled favorite sports to watch is divided into three portions. football represents 42 percent, baseball represents 33 percent, and soccer represents 25 percent. if 210 people said football was their favorite sport to watch, how many people were surveyed?
Answers: 1
Verify by substitution that each given function is a solution of the given differential equation.
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