![12. Find all the equilibrium points of the competing species model [2.5 marks] x = 0.6-0.2x2-0. Iy 13. Select the second-ord](http://img.homeworklib.com/questions/05bfc7b0-aa04-11ea-98bc-8f5b4856dd1d.png?x-oss-process=image/resize,w_560)
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12. Find all the equilibrium points of the competing species model [2.5 marks] x' = 0.6-0.2x2-0....
given y1=x is a solution of the following DEXX+2xy-2y=0, the second solution is x 2 e2...
given y1=x is a solution of the following DEXX+2xy-2y=0, the second solution is x 2 e2 Question 2 2 pts The differential equation whose general solution is Y=CCos(6x)+C2 Sin (V6 x) y" by 0 Oy -6y=0 y +6y=0 y"+6y'=0 2 pts Question 3 given that y1= x1 is a solution, if we use the reduction of order to solve the ODE 2x2 y + xy - 3y=0 we find that u= AXR+B (Ax512 - Ax+B Axe5124B
Find two power series solutions of the given differential equation about the ordinary point x =...
Find two power series solutions of the given differential
equation about the ordinary point x = 0. y′′ − 4xy′ + y = 0
Find two power series solutions of the given differential equation about the ordinary point x = 0. y!' - 4xy' + y = 0 Step 1 We are asked to find two power series solutions to the following homogenous linear second-order differential equation. y" - 4xy' + y = 0 By Theorem 6.2.1, we know two...
1. 10 points Given y(x) x 'is a solution to the differential equation x’y"+ 6xy'+6y=0 (x...
1. 10 points Given y(x) x 'is a solution to the differential equation x’y"+ 6xy'+6y=0 (x > 0), find a second linearly independent solution using reduction of order.
2. -13 points ZillDiffEQModAp111.1.011. 0/6 Submissions Used My Notes Verify that the indicated function is an...
2. -13 points ZillDiffEQModAp111.1.011. 0/6 Submissions Used My Notes Verify that the indicated function is an explicit solution of the given differential equation. Assume an appropriate intervall of definition for the solution. 6y + y = 0; y = e-x/6 When y = e-x/6 y'a Thus, in terms of x, 6y' + y = 3. -12 points ZillDiffEQModAp111.2.001. 0/6 Submissions Used My Notes Ask Your Teacher In this problem, y = 1/(1+ce) is a one-parameter family of solutions of the...
help with all except numbers 21-26 16. Solve the differential equation by using the Cauchy-Euler Equation 17. Find the solution to the given Initial Value Problem using Green's Theorem 0,y'...
help with all except numbers 21-26
16. Solve the differential equation by using the Cauchy-Euler Equation 17. Find the solution to the given Initial Value Problem using Green's Theorem 0,y'(0)s 0 y(0) y" + 6y' + 9y x, 18. Find the solution to the given Boundary Value Problem y" ty-1, y(O)0, y(1) 19. Solve the system of differential equations by systematic elimination. dy dt dt 20. Use any procedure in Chapter 4 to solve the differential equation subjected to the...
7 marks (4 marks) (3 marks) (a) Is the operator P(v) y'+2ty linear? (Show workings) (b) Find the ...
please answer question 1) to 3) fully step by step
7 marks (4 marks) (3 marks) (a) Is the operator P(v) y'+2ty linear? (Show workings) (b) Find the null space of the operator in (a) above. Question 2 5 marks Let P be a linear operator. Suppose that y is a particular solution to the equation Ply) = b. Prove that any solution to this equation can be written as y = Yo + yi for yo au clement of...
The Chebyshev equation of order p is, (1 2 p?y = 0. a Show that x = 1 and x = -1 are regular singular points and find t...
The Chebyshev equation of order p is, (1 2 p?y = 0. a Show that x = 1 and x = -1 are regular singular points and find the roots of the associated Euler's equations at each of these points. b) Find the first three non-zero terms in the two series solution about x = 1
The Chebyshev equation of order p is, (1 2 p?y = 0. a Show that x = 1 and x = -1 are regular...
Answer all questions (100 marks) 1. Given x(0) = 0 and transform. = 0, solve the...
Answer all questions (100 marks) 1. Given x(0) = 0 and transform. = 0, solve the following differential equation using Laplace d?x(t) dx +6 dt2 + 8x(t) = 2e-31 dt (20 marks) 2. Find the vo(t) in the network in Figure I using Laplace approach. 12 S 2 w O 1,(s) Ls) V.(5) Figure 1 (30 mrks)
Points) Use the differential equation (x-x- 12 following questions: (a) Find all singular points ...
points) Use the differential equation (x-x- 12 following questions: (a) Find all singular points of the differential equation. title diferential equation (ra-r-11-2r-w-0 to answer the (b) What is the radius of convergence for a power series solution about the point ro 0? About xo-4?
points) Use the differential equation (x-x- 12 following questions: (a) Find all singular points of the differential equation. title diferential equation (ra-r-11-2r-w-0 to answer the (b) What is the radius of convergence for a power series...
solve Question 6: Given that v(0) = 2 and dv(0)/dt = 4, solve the following second-order...
solve
Question 6: Given that v(0) = 2 and dv(0)/dt = 4, solve the following second-order differential equation d- du ( +54 + 60 = 10e-'u(t) dt 4 marks
given y1=x is a solution of the following DEXX+2xy-2y=0, the second solution is x 2 e2 Question 2 2 pts The differential equation whose general solution is Y=CCos(6x)+C2 Sin (V6 x) y" by 0 Oy -6y=0 y +6y=0 y"+6y'=0 2 pts Question 3 given that y1= x1 is a solution, if we use the reduction of order to solve the ODE 2x2 y + xy - 3y=0 we find that u= AXR+B (Ax512 - Ax+B Axe5124B
Find two power series solutions of the given differential
equation about the ordinary point x = 0. y′′ − 4xy′ + y = 0
Find two power series solutions of the given differential equation about the ordinary point x = 0. y!' - 4xy' + y = 0 Step 1 We are asked to find two power series solutions to the following homogenous linear second-order differential equation. y" - 4xy' + y = 0 By Theorem 6.2.1, we know two...
1. 10 points Given y(x) x 'is a solution to the differential equation x’y"+ 6xy'+6y=0 (x > 0), find a second linearly independent solution using reduction of order.
2. -13 points ZillDiffEQModAp111.1.011. 0/6 Submissions Used My Notes Verify that the indicated function is an explicit solution of the given differential equation. Assume an appropriate intervall of definition for the solution. 6y + y = 0; y = e-x/6 When y = e-x/6 y'a Thus, in terms of x, 6y' + y = 3. -12 points ZillDiffEQModAp111.2.001. 0/6 Submissions Used My Notes Ask Your Teacher In this problem, y = 1/(1+ce) is a one-parameter family of solutions of the...
help with all except numbers 21-26
16. Solve the differential equation by using the Cauchy-Euler Equation 17. Find the solution to the given Initial Value Problem using Green's Theorem 0,y'(0)s 0 y(0) y" + 6y' + 9y x, 18. Find the solution to the given Boundary Value Problem y" ty-1, y(O)0, y(1) 19. Solve the system of differential equations by systematic elimination. dy dt dt 20. Use any procedure in Chapter 4 to solve the differential equation subjected to the...
please answer question 1) to 3) fully step by step
7 marks (4 marks) (3 marks) (a) Is the operator P(v) y'+2ty linear? (Show workings) (b) Find the null space of the operator in (a) above. Question 2 5 marks Let P be a linear operator. Suppose that y is a particular solution to the equation Ply) = b. Prove that any solution to this equation can be written as y = Yo + yi for yo au clement of...
The Chebyshev equation of order p is, (1 2 p?y = 0. a Show that x = 1 and x = -1 are regular singular points and find the roots of the associated Euler's equations at each of these points. b) Find the first three non-zero terms in the two series solution about x = 1
The Chebyshev equation of order p is, (1 2 p?y = 0. a Show that x = 1 and x = -1 are regular...
Answer all questions (100 marks) 1. Given x(0) = 0 and transform. = 0, solve the following differential equation using Laplace d?x(t) dx +6 dt2 + 8x(t) = 2e-31 dt (20 marks) 2. Find the vo(t) in the network in Figure I using Laplace approach. 12 S 2 w O 1,(s) Ls) V.(5) Figure 1 (30 mrks)
points) Use the differential equation (x-x- 12 following questions: (a) Find all singular points of the differential equation. title diferential equation (ra-r-11-2r-w-0 to answer the (b) What is the radius of convergence for a power series solution about the point ro 0? About xo-4?
points) Use the differential equation (x-x- 12 following questions: (a) Find all singular points of the differential equation. title diferential equation (ra-r-11-2r-w-0 to answer the (b) What is the radius of convergence for a power series...
solve
Question 6: Given that v(0) = 2 and dv(0)/dt = 4, solve the following second-order differential equation d- du ( +54 + 60 = 10e-'u(t) dt 4 marks
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