4. Arfken, p. 372, Prob. 7.6.16. Recall That, For a General Linear Second Order ODE, y(x)+P(x)y'(x)+0(x)y(x)-0, Given a First Solution y, (x), a Second Solution Can Be Constructed Using the Wronskian Technique, Which Is exp-JdP(x,) M(x,) . For One Solution Being (, Find the Second Solution, y, (r), To This Specific ODE, Using the Wronskian Technique. Use the Second Solution In the ODE To Show That It Is a Solution.
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7.6.16 Given that one solution of 1m2 is R r", show that Eq. 7.67 predicts a second solution, R-r...
It's in Mathematical Methods for Physicists 7e, Arfken ch7.6 Other solutions (ODEs). Please help. Thank you. One solution of Hermite's differential equation 7.6.19 (a) for α = 0 is yi (x) = l...
It's in Mathematical Methods for Physicists 7e, Arfken ch7.6
Other solutions (ODEs).
Please help.
Thank you.
One solution of Hermite's differential equation 7.6.19 (a) for α = 0 is yi (x) = l. Find a second solution, y2(x), using Eq. (7.67). Show that your second solution is equivalent to yodd (Exercise 8.3.3). Find a second solution for α = 1, where yi (x) =x, using Eq. (7.67). Show that your second solution is equivalent to yeven (Exercise 8.3.3) (b)
One...
It's in Mathematical Methods for Physicists 7e, Arfken ch7.7 Inhomogeeous linear ODEs. Please help. Thank you. 7.7.1 If our linear, second-order ODE is inhomogeneous, tha is, of the form of Eq. (...
It's in Mathematical Methods for Physicists 7e, Arfken ch7.7
Inhomogeeous linear ODEs.
Please help.
Thank you.
7.7.1 If our linear, second-order ODE is inhomogeneous, tha is, of the form of Eq. (7.94), the most general solution is where yi and y2 are independent solutions of the homogeneous equation Show that yi(x)2()Fsds W[yi(s), y2()) Wyi(), y2(s) with Wlyxy2x)) the Wronskian of yi(s) and y2(s) Find the general solutions to the following inhomogeneous ODEs:
7.7.1 If our linear, second-order ODE is inhomogeneous,...
It's in Mathematical Methods for Physicists 7e, Arfken ch7.6 Other solutions (ODEs). Please help. Thank you....
It's in Mathematical Methods for Physicists 7e, Arfken ch7.6
Other solutions (ODEs).
Please help.
Thank you.
One solution of Hermite's differential equation 7.6.19 (a) for α = 0 is yi (x) = l. Find a second solution, y2(x), using Eq. (7.67). Show that your second solution is equivalent to yodd (Exercise 8.3.3). Find a second solution for α = 1, where yi (x) =x, using Eq. (7.67). Show that your second solution is equivalent to yeven (Exercise 8.3.3) (b)
Let A t be a continuous family of 2 × 2 matrices and let P t) be the matrix solution to the initi...
Let A t be a continuous family of 2 × 2 matrices and let P t) be the matrix solution to the initial value problem p for n x n matrices, but it's messier.) Show that A()P, P )-P-(The result can be proved detP(t) (detPo) exp(J0 TrA(s)ds How is this related to the Wronskian from second order differential equations? (Look back at your work on second order differential equations in mth165 or similar class, or look up the definition on...
7.6.26 It's in Mathematical Methods for Physicists 7e, Arfken Please help. Thank you so much. 7.6.26 (a) Show that...
7.6.26
It's in Mathematical Methods for Physicists 7e, Arfken
Please help.
Thank you so much.
7.6.26 (a) Show that has two solutions: (b) For α 0 the two linearly independent solutions of part (a) reduce to the single solution y o. Using Eq. (7.68) derive a second solution, Verify that y is indeed a solution. (c) Show that the second solution from part (b) may be obtained as a ing case from the two solutions of part (a): lim (...
Please show all work and steps! Would like to learn how! Given a second order linear...
Please show all work and
steps! Would like to learn how!
Given a second order linear homogeneous differential equation a2(x)y" + a1(x)y' + 20 (x)y = 0 we know that a fundamental set for this ODE consists of a pair linearly independent solutions Yı, Y2. But there are times when only one function, call it Yı, is available and we would like to find a second linearly independent solution. We can find Y2 using the method of reduction of order....
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
Need help with diff eq Determine the general solution of the given differential equation (Show your...
Need help with diff eq
Determine the general solution of the given differential equation (Show your work) 2x2y" – 4xy' +10y = 0 a) y = (x3 + c2x-1 b) y = (C1 + czln|x1)x3 c) y= claſicos ($71 In[xl) + cz|xpă sin ("ZI Inļxl) d) y = cz|x|3 cos ("7 In[xl) + cz|xl sin (977 1n\xl) e) y = cz\x{* cos(v11 In[xl) + czlxpă sin(V11 In[xl)
Show that Eq. 5.31 gives the value A = 2/L. To complete the solution for (x),...
Show that Eq. 5.31 gives the value A = 2/L.
To complete the solution for (x), we must determine the constant A by using the normalization condition given in Eq. 5.9, S V x) dx = 1. The integrand is zero in the regions - <x<0 and L <x<+co, so all that remains is (5.31) from which we find A = then 2/L. The complete wave function for 0 SXS Lis
3. First, here is a summary of the method of variation of parameters (Braun 2.4). Given a general...
3. First, here is a summary of the method of variation of parameters (Braun 2.4). Given a general linear second order ODE of the form with p, q and g continuous on some interval I that contains the initial condition, and given that you have a fundamental solution set gi(t) and y2(t) to the homogeneous problem Ly]-0, one can find a particular solution as follows. [Follow along on pg. 154 of Braun] . Let yp(t) = ui (t)n(t) + u2(t)m(t),...
It's in Mathematical Methods for Physicists 7e, Arfken ch7.6
Other solutions (ODEs).
Please help.
Thank you.
One solution of Hermite's differential equation 7.6.19 (a) for α = 0 is yi (x) = l. Find a second solution, y2(x), using Eq. (7.67). Show that your second solution is equivalent to yodd (Exercise 8.3.3). Find a second solution for α = 1, where yi (x) =x, using Eq. (7.67). Show that your second solution is equivalent to yeven (Exercise 8.3.3) (b)
One...
It's in Mathematical Methods for Physicists 7e, Arfken ch7.7
Inhomogeeous linear ODEs.
Please help.
Thank you.
7.7.1 If our linear, second-order ODE is inhomogeneous, tha is, of the form of Eq. (7.94), the most general solution is where yi and y2 are independent solutions of the homogeneous equation Show that yi(x)2()Fsds W[yi(s), y2()) Wyi(), y2(s) with Wlyxy2x)) the Wronskian of yi(s) and y2(s) Find the general solutions to the following inhomogeneous ODEs:
7.7.1 If our linear, second-order ODE is inhomogeneous,...
It's in Mathematical Methods for Physicists 7e, Arfken ch7.6
Other solutions (ODEs).
Please help.
Thank you.
One solution of Hermite's differential equation 7.6.19 (a) for α = 0 is yi (x) = l. Find a second solution, y2(x), using Eq. (7.67). Show that your second solution is equivalent to yodd (Exercise 8.3.3). Find a second solution for α = 1, where yi (x) =x, using Eq. (7.67). Show that your second solution is equivalent to yeven (Exercise 8.3.3) (b)
Let A t be a continuous family of 2 × 2 matrices and let P t) be the matrix solution to the initial value problem p for n x n matrices, but it's messier.) Show that A()P, P )-P-(The result can be proved detP(t) (detPo) exp(J0 TrA(s)ds How is this related to the Wronskian from second order differential equations? (Look back at your work on second order differential equations in mth165 or similar class, or look up the definition on...
7.6.26
It's in Mathematical Methods for Physicists 7e, Arfken
Please help.
Thank you so much.
7.6.26 (a) Show that has two solutions: (b) For α 0 the two linearly independent solutions of part (a) reduce to the single solution y o. Using Eq. (7.68) derive a second solution, Verify that y is indeed a solution. (c) Show that the second solution from part (b) may be obtained as a ing case from the two solutions of part (a): lim (...
Please show all work and
steps! Would like to learn how!
Given a second order linear homogeneous differential equation a2(x)y" + a1(x)y' + 20 (x)y = 0 we know that a fundamental set for this ODE consists of a pair linearly independent solutions Yı, Y2. But there are times when only one function, call it Yı, is available and we would like to find a second linearly independent solution. We can find Y2 using the method of reduction of order....
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
Need help with diff eq
Determine the general solution of the given differential equation (Show your work) 2x2y" – 4xy' +10y = 0 a) y = (x3 + c2x-1 b) y = (C1 + czln|x1)x3 c) y= claſicos ($71 In[xl) + cz|xpă sin ("ZI Inļxl) d) y = cz|x|3 cos ("7 In[xl) + cz|xl sin (977 1n\xl) e) y = cz\x{* cos(v11 In[xl) + czlxpă sin(V11 In[xl)
Show that Eq. 5.31 gives the value A = 2/L.
To complete the solution for (x), we must determine the constant A by using the normalization condition given in Eq. 5.9, S V x) dx = 1. The integrand is zero in the regions - <x<0 and L <x<+co, so all that remains is (5.31) from which we find A = then 2/L. The complete wave function for 0 SXS Lis
3. First, here is a summary of the method of variation of parameters (Braun 2.4). Given a general linear second order ODE of the form with p, q and g continuous on some interval I that contains the initial condition, and given that you have a fundamental solution set gi(t) and y2(t) to the homogeneous problem Ly]-0, one can find a particular solution as follows. [Follow along on pg. 154 of Braun] . Let yp(t) = ui (t)n(t) + u2(t)m(t),...
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