[13] For each of the following equations, find general solutions; solve the initial value problem with initial condition x₁ (0) = -1, x₂ (0) = 2; • sketch the phase portrait, identify the type of each equilibrium, and determine the stability of each equilibrium. d +4x₂ -5 0 (a) (18]-[45] OE-736] *-[72] = (b) (c) x' X dt X2 +5x₂ 4 X2 0

Q: (c) A function y(t) is a solution of y' + ky = 0. Sup find: (i) k (ii) y(t)

A: It is differential equation problem

Q: Solve the initial value problem. (y)(1/2)dx+(x-8)dy=0, y(9)=16

A:

Q: Consider the differential equation and y' = y² - 5y + 6. (a) Find the equilibrium points of the…

A: Phase line: The graphical representation of all the solutions of the first order differential…

Q: Solve the initial value problem (x² + 3y²)dx – 2xydy = 0 ;У(2) — 6

A:

Q: y′= 2x/1+2y, y(2)=0 Find an explicit solution for the initial value problem. Plot the graph…

A: Differential equation

Q: Solve simultaneously y (t) = 1 – a"(t) z' (t) = 2y (t) x(t) = -yr(t) where x (0) = 2, x' (0) = –1, y…

A:

Q: Find the stationary points of y = = (x² – 2x³)e²x. Note: you must give exact values do not…

A:

Q: To find v,(x=0.1) yn-1-0.1+ (0.1)2-1(0.1)" +급(01).-0.909675 To find y2(x=0.2) Expansion around x0 HW…

A:

Q: b. Solve the initial value problem: f (x)= sin x +e2, f(0) = 4 1 f (0) 2

A: Given: f''(x) = sin x + e2x, f(0) = 14 and f'(0) =12

Q: Consider the differential equation: (x + 1) dy -y + 10 dx (a) Is the equation separable? If yes,…

A: The given equation is, x+1dydx=-y+10.

Q: B1(b): Solve the initial value problem : f'(x)= x!0 + 12x + 19 and f(0) = 1.

A:

Q: a + by(t) = f(t), dy(t) dt (a) Solve this equation for a = 1, b = 3 and f(t) = 10a? (b) Solve this…

A:

Q: Solve (x² 1 + 2y) dx + (1 - x²) dy = 0; when x = 2, y = 1 1) (x + 1 + 2 ln x 1|) b. (x + 1) y = (x −…

A: Given: x2-1+2ydx + 1-x2dy = 0 , when x=2, y=1. Solve the given differential equation. Concept used:…

Q: hildsmath) A 1800 L tank contains 500 L of water with a salt concentration of 20 g/L. Water with a…

A:

Q: (2.2) Consider the differential equation y = (6x – 2y – 3)1º (1) By making the change of variable…

A:

Q: e y1(t) – 6yl(t) + 8y(t) = e2t + sin (t) ; y(0) = 0 ; yl(0) = 1 %3D

A:

Q: f(x) Consider the autonomous differential equation æ' f(x) with function f(x) that has the graph…

A:

Q: d a first-order, linear initial-value problem that has the given function as a solution. y(t)= 5e-

A: Introduction: A differential equation is an equation that contains the derivative of an unknown…

Q: (d) Solve the differential equation given that y(0) = 1. (ex + y)dx +(2+x+ye³)dy = 0,

A:

Q: Solve the initial value problem: (2ye2xy – 2) dx + (2xe2*y +) dy = 0; y(1) = 1 %3D y²

A:

Q: Question 4 Consider the data given in the following table 0.45 0.46 0.48 0.50 0.52 0.54 0.56 057 foo…

A:

Q: Solve the equation (2xy+ y) dæ + (x² – x) dy = 0. - O y = cx(x +1)° + 2x O y = cx(x+1)¯³ – 2 II O y…

A:

Q: dy The equation - y = x², where y(0) = 0 dx a. is homogenous and nonlinear, and has infinite…

A:

Q: Solve the following initial value problem (y)dx+(y4-4x)dy=0 with x(2)=5/2.  For your final answer,…

A: Given,      (y)dx+(y4-4x)dy=0  and   x2=52

Q: dx + 2y−1xdy = 2x2y2dy, y(1) = 1 Solve the initial value problem

A:

Q: (x5 + y5) dx + (5xy4–2y+1) dx = 0 (a) Show that the given differential equation is exact. (b) Solve…

A:

Q: For each of the differential equations below, find the critical points, draw a phase diagram, and…

A:

Q: Consider the logistic equation (a) Find the solution satisfying y₁ (0) = 8 and y/₂(0) = -5. yi(t) =…

A:

Q: Find the equilibrium solutions and analyze the stability using the phase diagram.

A: Step 1:Step 2: