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QUESTION 3 Find explicit solutions of each of the ODEs given below dy 2xy 3 dx...
Problem 3. Consider the following continuous differential equation dx dt = αx − 2xy dy dt...
Problem 3. Consider the following continuous differential equation dx dt = αx − 2xy dy dt = 3xy − y 3a (5 pts): Find the steady states of the system. 3b (15 pts): Linearize the model about each of the fixed points and determine the type of stability. 3b (15 pts): Draw the phase portrait for this system, including nullclines, flow trajectories, and all fixed points. Problem 2 (25 pts): Two-dimensional linear ODEs For the following linear systems, identify the...
Please show steps. Given 3 dy/dx + 2xy^2 = 5x^2 - x + 1, where y(0)...
Please show steps.
Given 3 dy/dx + 2xy^2 = 5x^2 - x + 1, where y(0) = 5 and using a step size of dx = 1, the value of y(1) using Euler's method is most nearly 5.333 1.010 -0.499 17.822 Given 3 dy/dx + 2xy^2 = 5x^2 - x + 1, where y(0) = 5 and using a step size of dx = 1, the value of y(1) using Runge-Kutta 4^th order method is most nearly 5.333 1.010 -0.499...
Find an explicit solution of the given initial-value problem. ✓ 3 ✓ 1 - y2 dx...
Find an explicit solution of the given initial-value problem. ✓ 3 ✓ 1 - y2 dx - V1 - x? dy = 0, y(O) = 2
15. (2xy + y^2 ) dx + (2xy + x^2 − 2x 2y^2 − 2xy^3 ) dy = 0
15. (2xy + y^2 ) dx + (2xy + x^2 − 2x 2y^2 − 2xy^3 ) dy = 0
Find the solution to the initial value problem dy 6xy + y2 + (3x2 + 2xy...
Find the solution to the initial value problem dy 6xy + y2 + (3x2 + 2xy + 2y) dx =0 y(1) = 3 OA x+y + 2xy2 + y2 + x = 31 OB. 6xy + 2y2 + x = 37 3x²y + 2x2y + x3 + 2x2 + 2y = 24 OD 3x2y + xy2 + y2 = 27 ОЕ xºy + x2y2 + y2 + x = 22
3. Find the general solutions for the following homogeneous ODEs. dºy.dy + y = 0 a)...
3. Find the general solutions for the following homogeneous ODEs. dºy.dy + y = 0 a) dx2 dx d²y b) dx2 4y = 0 a) d²y dy + dx² dx = 0
Solve the given initial-value problem. (x + y)2 dx + (2xy + x2 – 8) dy...
Solve the given initial-value problem. (x + y)2 dx + (2xy + x2 – 8) dy = 0, y(1) = 1 (x + y)3 (x + y)2 - 8x = -1
Evaluate ∫∫∫T 2xy dx dy dz where T is the solid in the first octant bounded...
Evaluate ∫∫∫T 2xy dx dy dz where T is the solid in the first octant bounded above by the cylinder z = 4 − x^2 below by the x, y-plane, and on the sides by the planes x =0, y = 2x and y = 4. Answer: ∫ (4, 0) ∫ (y/2, 0) ∫ (4−x^2, 0) 2xy dz dx dy = ∫ (2, 0) ∫ (4, 2x) ∫ (4−x^2, 0) 2xy dz dy dx = 128/3
3. (25 points) Given a series of ODES: dy = 6e– y2 +224/7 = 62 +...
3. (25 points) Given a series of ODES: dy = 6e– y2 +224/7 = 62 + 3y Given initial conditions y(0)=0, 2(0)=1, and I = 1; dra dx dx x=0 solve the system using 2nd-order Runge:Kutta method (Heun's method) with step size of h = 1. dy (Hint: Treat- dy dz as separate ODES) dx2
In problems 7 and 8 find the solution of the given initial value problem in explicit...
In problems 7 and 8 find the solution of the given initial value problem in explicit form: 7. sin 2.x dx + cos 3y dy = 0, y /2) = 1/3. 8. y' (1-22)/2 dy = arcsin x dx, y(0) = 1.
Please show steps.
Given 3 dy/dx + 2xy^2 = 5x^2 - x + 1, where y(0) = 5 and using a step size of dx = 1, the value of y(1) using Euler's method is most nearly 5.333 1.010 -0.499 17.822 Given 3 dy/dx + 2xy^2 = 5x^2 - x + 1, where y(0) = 5 and using a step size of dx = 1, the value of y(1) using Runge-Kutta 4^th order method is most nearly 5.333 1.010 -0.499...
Find an explicit solution of the given initial-value problem. ✓ 3 ✓ 1 - y2 dx - V1 - x? dy = 0, y(O) = 2
Find the solution to the initial value problem dy 6xy + y2 + (3x2 + 2xy + 2y) dx =0 y(1) = 3 OA x+y + 2xy2 + y2 + x = 31 OB. 6xy + 2y2 + x = 37 3x²y + 2x2y + x3 + 2x2 + 2y = 24 OD 3x2y + xy2 + y2 = 27 ОЕ xºy + x2y2 + y2 + x = 22
3. Find the general solutions for the following homogeneous ODEs. dºy.dy + y = 0 a) dx2 dx d²y b) dx2 4y = 0 a) d²y dy + dx² dx = 0
Solve the given initial-value problem. (x + y)2 dx + (2xy + x2 – 8) dy = 0, y(1) = 1 (x + y)3 (x + y)2 - 8x = -1
3. (25 points) Given a series of ODES: dy = 6e– y2 +224/7 = 62 + 3y Given initial conditions y(0)=0, 2(0)=1, and I = 1; dra dx dx x=0 solve the system using 2nd-order Runge:Kutta method (Heun's method) with step size of h = 1. dy (Hint: Treat- dy dz as separate ODES) dx2
In problems 7 and 8 find the solution of the given initial value problem in explicit form: 7. sin 2.x dx + cos 3y dy = 0, y /2) = 1/3. 8. y' (1-22)/2 dy = arcsin x dx, y(0) = 1.
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