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Question 1 Given the differential equation X d2 dx2 -2 X-2 ( ) = 0, then...
3. [8 marks] Consider the differential equation d2 dx2 Solve the regular perturbation problem wit...
Can someone help show how to answer this question. Thanks in
advance.
3. [8 marks] Consider the differential equation d2 dx2 Solve the regular perturbation problem with error of order 0(e2),ie. up to and including terms of 0(e)
3. [8 marks] Consider the differential equation d2 dx2 Solve the regular perturbation problem with error of order 0(e2),ie. up to and including terms of 0(e)
1. Determine the solution to the following differential equation (implicit if necessary): 2. Determine the general...
1. Determine the solution to the following differential equation (implicit if necessary): 2. Determine the general solution, y(x), to the following differential equations [use synthetic division to solve a), b), and d)]. Show all your work dx3dx2 dx b)@y-4ーー3을y+18y = 0 d2 dx2 dx3 dx dx2 dx + 2-10 dy, dy _ y = 0 dx dx x f) χ +dy=kx where k is a constant dx2 dx
Зрт Question 1 f (x + y)da - ady=0 The solution of the Initial-Value Problem (IVP)...
Зрт Question 1 f (x + y)da - ady=0 The solution of the Initial-Value Problem (IVP) 1 y(1) = 0 is given by Oy= (x + y) In a Oy = x In a Oy= « ln(x + y) 3 = teº-1 None of them n Question 2 3 pts The general solution of the first order non-homogeneous linear differential equation with variable dy coefficients (a +1) + xy = e > -1 equals da 3 Oy= e-* [C(x2 -...
Question 2 3 pts The general solution of the first order non-homogeneous linear differential dy equation...
Question 2 3 pts The general solution of the first order non-homogeneous linear differential dy equation with variable coefficients (x + 1) + xy = e-, x>-1 dx equals y=e-* (C(x + 1) - 1], where C is an arbitrary constant. Oy=e" (C(x - 1) + 1], where is an arbitrary constant. Oy=e" (C(x2 – 1) + 1], where C is an arbitrary constant. None of them O y=e" (C(x2 – 1) +1], where C is an arbitrary constant.
Solve the differential equation (D2 + 1) y = x cscº x.
Solve the differential equation (D2 + 1) y = x cscº x.
4. Consider the homogeneous differential equation dy d y dy-y=0 dx3 + dx2 dx - y...
4. Consider the homogeneous differential equation dy d y dy-y=0 dx3 + dx2 dx - y (a) Show that 01 (C) = e is a solution. (b) Show that 02 (2) = e-* is a solution. (c) Show that 03 (x) = xe-" is a solution. (d) Determine the general solution to this homogeneous differential equation. (e) Show that p (2) = xe" is a particular solution to the differential equation dy dy dy dx3 d.x2 - y = 4e*...
2. Find the solution of the second order differential equations: d2 +y = 0, y(T/3) =...
2. Find the solution of the second order differential equations: d2 +y = 0, y(T/3) = 0, y'(T/3) = 4 a. dx2 b. Y" - 8y' + 16y = 0, y(0) = 1, y(1) = 0
Question 1 3 pts The solution of the Initial-Value Problem (IVP) S (x + y)dx –...
Question 1 3 pts The solution of the Initial-Value Problem (IVP) S (x + y)dx – «dy = 0 is given by 1 y(1) = 0 Oy=det-1 - 1 Oy= < ln(x + y) Oy= (x + y) In x Oy= < In x None of them Question 2 3 pts The general solution of the first order non-homogeneous linear differential equation with variable coefficients dy (x + 1) + xy = e-">-1 equals dx 2 Oy=e* (C(x - 1)...
Given y'"- y" - 4y'- 6y=0 (1) , identify Differential Operator L of (1). OL=D3-D2 -...
Given y'"- y" - 4y'- 6y=0 (1) , identify Differential Operator L of (1). OL=D3-D2 - 4D - 6 o L = (D - 3)(D2 + 2D + 2) O Both of them are correct! None of them
If S= {e*, e*, xe* is a fundamental solution set for the homogenous differential equation with...
If S= {e*, e*, xe* is a fundamental solution set for the homogenous differential equation with constant coefficients dy a2 dy +a dx2 d y + a y 0, dx dx find the values of a ,i= 0, 1, 2, 3 (5 markah/marks) Dengan nilai yang diperolehi dari (a), selesaikanlah masalah nilai awal yang berikut: (b) day 2 (1+2e) d2 y a a dx dy ax a ax dengan 0)1,y' (0)- 2,y (0)-3. By using the values obtained in (a),...
Can someone help show how to answer this question. Thanks in
advance.
3. [8 marks] Consider the differential equation d2 dx2 Solve the regular perturbation problem with error of order 0(e2),ie. up to and including terms of 0(e)
3. [8 marks] Consider the differential equation d2 dx2 Solve the regular perturbation problem with error of order 0(e2),ie. up to and including terms of 0(e)
1. Determine the solution to the following differential equation (implicit if necessary): 2. Determine the general solution, y(x), to the following differential equations [use synthetic division to solve a), b), and d)]. Show all your work dx3dx2 dx b)@y-4ーー3을y+18y = 0 d2 dx2 dx3 dx dx2 dx + 2-10 dy, dy _ y = 0 dx dx x f) χ +dy=kx where k is a constant dx2 dx
Зрт Question 1 f (x + y)da - ady=0 The solution of the Initial-Value Problem (IVP) 1 y(1) = 0 is given by Oy= (x + y) In a Oy = x In a Oy= « ln(x + y) 3 = teº-1 None of them n Question 2 3 pts The general solution of the first order non-homogeneous linear differential equation with variable dy coefficients (a +1) + xy = e > -1 equals da 3 Oy= e-* [C(x2 -...
Question 2 3 pts The general solution of the first order non-homogeneous linear differential dy equation with variable coefficients (x + 1) + xy = e-, x>-1 dx equals y=e-* (C(x + 1) - 1], where C is an arbitrary constant. Oy=e" (C(x - 1) + 1], where is an arbitrary constant. Oy=e" (C(x2 – 1) + 1], where C is an arbitrary constant. None of them O y=e" (C(x2 – 1) +1], where C is an arbitrary constant.
Solve the differential equation (D2 + 1) y = x cscº x.
4. Consider the homogeneous differential equation dy d y dy-y=0 dx3 + dx2 dx - y (a) Show that 01 (C) = e is a solution. (b) Show that 02 (2) = e-* is a solution. (c) Show that 03 (x) = xe-" is a solution. (d) Determine the general solution to this homogeneous differential equation. (e) Show that p (2) = xe" is a particular solution to the differential equation dy dy dy dx3 d.x2 - y = 4e*...
2. Find the solution of the second order differential equations: d2 +y = 0, y(T/3) = 0, y'(T/3) = 4 a. dx2 b. Y" - 8y' + 16y = 0, y(0) = 1, y(1) = 0
Question 1 3 pts The solution of the Initial-Value Problem (IVP) S (x + y)dx – «dy = 0 is given by 1 y(1) = 0 Oy=det-1 - 1 Oy= < ln(x + y) Oy= (x + y) In x Oy= < In x None of them Question 2 3 pts The general solution of the first order non-homogeneous linear differential equation with variable coefficients dy (x + 1) + xy = e-">-1 equals dx 2 Oy=e* (C(x - 1)...
Given y'"- y" - 4y'- 6y=0 (1) , identify Differential Operator L of (1). OL=D3-D2 - 4D - 6 o L = (D - 3)(D2 + 2D + 2) O Both of them are correct! None of them
If S= {e*, e*, xe* is a fundamental solution set for the homogenous differential equation with constant coefficients dy a2 dy +a dx2 d y + a y 0, dx dx find the values of a ,i= 0, 1, 2, 3 (5 markah/marks) Dengan nilai yang diperolehi dari (a), selesaikanlah masalah nilai awal yang berikut: (b) day 2 (1+2e) d2 y a a dx dy ax a ax dengan 0)1,y' (0)- 2,y (0)-3. By using the values obtained in (a),...
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