sketch and describe the phase portrait of each of each of the following systems Ip dt IP dt 1 . || dy || a) c) dr dt IP dt -y || || dt b) my subject is differential equation d) 2. ||

Q: 11) Calculate the Jacobian, J, for the change of variables x = u cos(0) - v sin(e) and yusin(0) + v…

A: The objective of this question is to calculate the Jacobian of the transformation from the variables…

Q: - 11) Calculate the Jacobian, J, for the change of variables x = u cos(0) – v sin(0) and yu sin(0) +…

A: The objective of this question is to calculate the Jacobian of the transformation from the variables…

Q: 3) A hot cup of tea has temperature T(1) = 198 °F, one minute after it has been sitting on the…

A: To calculate the local linearization of the temperature at t = 1.

Q: : )-+(÷), zw= (C) dx 1 et %3D dt 1 (: :)-+(-), -= (C) dx dt 1

A: Given dxdt=0110 x +ete-t Here let take A= 0110A-λI=-λ11-λ=0λ2-1=0λ=±1 Hence the eigen vector for 1…

Q: 2. Find a function f and a number a such that f(t) -dt = tanx. Give proper reasoning.

A:

Q: de Consider a model: = 1- cos 0 – ÷(1 + cos 0) dt (a) Determine the equilibrium points for this…

A: We are given, dθdt=1-cosθ -13(1+cos θ) Condition of Equilibrium: dθdt=0 ⇒1-cos θ-13(1+cos θ)=0⇒1-cos…

Q: - 11) Calculate the Jacobian, J, for the change of variables x = u cos(0) – v sin(0) and yu sin(0) +…

A: The objective of this question is to calculate the Jacobian of the transformation from the variables…

Q: Example: Sketch the direction field for the equation y' = y – t over the square -2 < t, y < 2, then…

A: The direction field is a graph of small line segments passing through various points whose slope is…

Q: - 11) Calculate the Jacobian, J, for the change of variables x = u cos(0) – v sin(0) and yu sin(0) +…

A: The objective of this question is to calculate the Jacobian of the transformation from the variables…

Q: 7 dt, where x> 2 Find dx for y = J 31+7 3

A: We shall use the Newton Leibniz formula

Q: ) Find f(t) if f(t) dt : = x sin 6x. A) 0 B) 6 C) n D) 6t

A: According to function,∫0xft dt = x sin 6x

Q: Q 2. Determine dt (i) J." -t2 4 (ii) ſe-t sin tdt. 4 (iii) J 73_2x² – 7x–4 -2х? —7х-4

A:

Q: O Đ 11) Calculate the Jacobian, J, for the change of variables x = u cos(0) -v sin(e) and y = u…

A: The objective of this question is to calculate the Jacobian of the transformation from the variables…

Q: 11 FCF)dt= fCx) dx =- 43 then 1.

A:

Q: O Đ 11) Calculate the Jacobian, J, for the change of variables x = u cos(0) -v sin(e) and y = u…

A: The objective of this question is to calculate the Jacobian of the transformation from the variables…

Q: 11) Calculate the Jacobian, J, for the change of variables x = u cos(e) - v sin(e) and y = u sin(0)…

A: The objective of this question is to calculate the Jacobian of the transformation from the variables…

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.