1. For each ODE below give the order, indicate the dependent and independent variables, and whether the DE is linear or nonlinear. (a) Shortest time problem, Galileo 1630: 2 dy y |1+ dr = C (b) Van der Pol's equation, triode vacuum tube: dy – 0.1(1 – y²). dy + 9y = 0 d.x %3D | dx? (e) 3 dar = t3 + xt dt dy (d) dx? dy = COS x - dx dy (e) + sin x – y = 0 dx

Q: Let y (t) be the solution of the initial value problem y"-4y +5y =e-2t 1 y (0) and y(0) = 17 %3D 17…

A: To find  The asymptotic behaviours as t tends to infinity.

Q: 1. Classify the following equations whether ordinary or partial, linear or non-linear, and give its…

A: (A) Given- xd2ydt2-yd2xdt2=c To classify- The above equations whether ordinary or partial, linear or…

Q: 4. Solve the following problem over the interval from x 0 to 1 using a step size of 0.25 where y(0)…

A: 4)

Q: 9. Let y (t) be the solution of the initial value problem y" – 4y + 5y = e=2t y (0) = 2 and y (0) =…

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Q: Example 10.14. Apply Runge's method to find an approximate value of y when x= 0.2, given that dy/dx…

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Q: Consider the ODE y' = y(1 – 4) • What is the order of the D.E.? Is it a linear or a non linear D.E.?…

A: Since you have posted a question with multiple sub-parts, we will solve the first three subparts for…

Q: Example 10.15. Apply Runge-Kutta fourth order method to find an approximate value of y when x = 0.2…

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Q: 1. Consider the ODE y In y dx – xdy = 0 With initial condition: y(2) = e a. Determine the general…

A: The complete solutions are given below

Q: 2 .2 Gun barrel. Solve y" + y = 1 – 12/1 if 0 s tST and 0 if t → ; here, y(0) = 0, y'(0) = 0. This…

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Q: For each of the following initial value problems, find the general solution of the ODE and the…

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Q: Consider the Lotka-Volterra predator-prey model defined by dx = -0.1x + 0.02xy dt dy = 0.2y –…

A: The solution is given below

Q: 4. Find C1, C2, and C3 so that the given functions will satisfy the prescribed initial conditions.…

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Q: 3. 3. Using Euler's numerical method, solve the following. From x= 0 to 1.4 using a step-size (h) =…

A: Given dydt=x-y, dxdt=x+2y and h=0.25, y0=2, x0=1

Q: The following problem involves an equation of the form dt = f(y). Sketch the graph of f(y) versus y,…

A: Given: d/dt=f(y) dy/dt=e^(-2y)-1

Q: 16 Q4- Solve the following system of ODE dx dt Eaux"> dy dt = y + 1 =x+1

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Q: can i get step by step help please

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Q: Use the information given in Figure 1 to construct a mathematical model for the number of kilograms…

A: Let consider the figure

Q: Solve the following system of equations using ode45. dy = -4y, – 2y2 + cos(t) + 4 sin(t), y,(0) = 0…

A: We will solve this problem using MATLAB with ode45. The code and corresponding solution curves are…

Q: Which of the following is the c value obtained for the special solution of the equation y'=ex+y…

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Q: 1. For each of the following, state whether the equation is ordinary or partial, linear or…

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Q: (64 – 2) dy = 1, y(0) = 9 Solve the initial-value problem for y as a function of x. %3D da

A: We need to solve the initial-value problem 64-x2 dydx=1, y0=9 for y as a function of x. So,…

Q: 4(a)Verify that the equation y = In x – Iny is an implicit solution of the IVP, ydx = x(y + 1)dy…

A: Ans:   4a we have to verify that the equation             y=lnx-lny  is an implicit  solution  of…

Q: Consider the following initial-value problem (IVP): dy x dx = y - x dx y(1) = 1 A.5.a. Find the…

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Q: 10) Solve the linear nonhomogeneous equation for the general solution. 2e* y" – y =- ex + e-x Hint:…

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Q: Solve the following problem over the interval from x=0 to 1 using a step size of 0.25 where y(0) = .…

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Q: Solve the ODE x²y" + xy' +| y = 0 about a singular point 16

A: We need to solve ODE.

Q: If the roots of the auxiliary equation of a second order linear homogeous ODE are k1 >0 and -k2 < 0,…

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Q: 9. Let y (t) be the solution of the initial value problem y" – 4y' + 5y = e-2t 1 y (0) and y' (0) 17…

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Q: Proceed as in Example 6 in Section 2.3 to solve the given initial-value problem. dy + y = f(x), y(0)…

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Q: 25.2 Solve the following problem over the interval from x = 0 to 1 using a step size of 0.25 where…

A: We can solve this using midpoint's method

Q: Solve for the Y(s) of a given function that is in terms of y(t) with the corresponding initial value…

A: There is some problem in the options given according to me the solution of given question is given…

Q: Example 10.22. Using Runge-Kutta method of order 4, find y for x = 0.1, 0.2, 0.3 given that dy/dx =…

A: Here, we need to use the Runge-Kutta method and Milne's method.

Q: Example find y (1) if dy y (1) if dy = 1/(x-Y) ; Y(0) = 1 dx (Use h=1) using Eulers method and using…

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Q: 2. Find a particular solution to each of these ODES by using the method of variation of parameters:…

A: Note: as per our guidelines we have to solve 1st question. So please repost other questiin . sorry…

Q: 10. Solve for the Y(s) of a given function that is in terms of y(t) with the corresponding initial…

A: Let's find.

Q: 23 3. Determine whether the function y(x) = 2sin4x is a solution to the initial value problem of y"…

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Q: Consider the following first-order ODE: dy = yx - x from x = 0 to x = 1.8 with y(0) = 1 dx a) Solve…

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Q: Plot the solution of the following second-order ODE ÿ + 1.5 (y² - 1) y + y = 0 on the interval 0 ≤ t…

A: As per the question we are given a secondary order nonlinear system (van der pol oscillator) y'' +…

Q: Find a particular solution to the ODE: y"+ y' – 2y = e* cos(2t) Yp(t) =

A: Given:  y''+y'-2y=e2t cos2t To Find:  To find the particular solution to the given ODE.ypt=?

Q: Which of the following graphs shows the solution of the initial value problem dy -x, y = 1 when x =…

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Q: 7. State whether the equation is ordinary or partial, linear or nonlinear, and give its order. * ()…

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Q: What is the largest step-size that can be used for a stable solution to the follo higher-order ODE…

A: Given:

Q: Consider the cascade of two tanks shown in Fig. 1.5.5, with V1 = 100 (gal) and V2 = 200 (gal) the…

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Q: 1. Use the classical fourth-order Runge-Kufta method to solve the ODE 9 dx dy -1.2y + 7e-0.3x from…

A: Given differential equation is: dydx=fx,y=−1.2y+7e−0.3x Initial condition: x0,y0=0,3 To approximate…

Q: the relationship between aphids, A, ( prey) and ladybugs, L, (preditor) can be described as follows:…

A: the critical point is find by comparing the derivative to zero.

Q: dy (b) kv. A constant

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Q: (j) Suppose that the solution of the initial value problem u" + u = 0.5 cost, u(0) = 0, u'(0) = 0 is…

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Q: If U = x y, find dU/dt if x* + y = t and x + y° = f

A: Given U = x3yx5+y = t                                    (1)x2+y3 = t2…

Q: Let y(x) be the solution of y' = y − 4x such that y(1) = 1. Using a step size of 0.5, set y0 =…

A: I am attaching a picture where you will get step by step solution first I write the formula of euler…

Q: Example 10.33. Applying Euler's method to the equation dyldx = Ay, given y(x) = yo %3D determine its…

A: Here, we need to use Euler's Method to solve given problem.

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.