Homework Answers
(1 point) Find the solution of x2y" + 5xy + (4 + 3x)y = 0, x...
(1 point) Find the solution of x2y" + 5xy + (4 + 3x)y = 0, x > 0 of the form Yi = x" Ž Cpx”, n=0 where co = : 1. Enter r = Cn = n = 1,2,3,...
(1 point) Find the solution of xy" + 5xy' + (4 + 1x)y = 0, x...
(1 point) Find the solution of xy" + 5xy' + (4 + 1x)y = 0, x > 0 of the form Yi = x n=0 where co = 1. Enter r = -2 Cn = - n= 1,2,3,...
(1 point) Find the solution of x²y" + 5xy' + (4 – 3x) y = 0,...
(1 point) Find the solution of x²y" + 5xy' + (4 – 3x) y = 0, x > 0 of the form y=x" Wazek, k=0 where ao = 1. r = help (numbers) ak = , k=1,2,3,... help (formulas)
Find a general solution to the given Cauchy-Euler equation for t> 0. 12d²y dy + 2t-...
Find a general solution to the given Cauchy-Euler equation for t> 0. 12d²y dy + 2t- dt - 6y = 0 dt² The general solution is y(t) =
4. At right, the point charges 2 4x are fixed on the y axis Note In...
4. At right, the point charges 2 4x are fixed on the y axis Note In this problem, let k 1/4neo a. Show that the magnitude of the resultant electric field at point P can be expressed in the form: Ep (2kg/x2) ( (a2/x2)-5/2 - 1) b. Show that in the case where x >» a the magnitude of resultant electric field at point P can be approximated by Hint: make use of the approximation (1 + α)N is valid...
Find the Laplace Transform of f(t)= - lifts 4; f(t) = 1 if t> 4.
Find the Laplace Transform of f(t)= - lifts 4; f(t) = 1 if t> 4.
Solve y'' +9y = $(t – 6), y(0) = y'(0) = 0 g(t) = for t...
Solve y'' +9y = $(t – 6), y(0) = y'(0) = 0 g(t) = for t < 6 for t > 6
3. [10pts] Consider the DE: xy" + 7xy' + Ty = 0. (a) Find the roots...
3. [10pts] Consider the DE: xy" + 7xy' + Ty = 0. (a) Find the roots rı and r2 of the indicial equation of the DE (with rı >r2). r = r2 = Solution: (b) If we use Frobenius method to solve the DE, we obtain for the largest indicial root and for n > 0, a recurrence acn relation of the form Cn+1 where a and b are constants. Find a and b. m11
dx Determine x= f(t) for (t? +4t) 4x + 4,t> 0; f(1) = 3. dt For...
dx Determine x= f(t) for (t? +4t) 4x + 4,t> 0; f(1) = 3. dt For (1? + 4t) dx dt = 4x +4, x= f(t) =
[10] 1. Solve the first-order equation Tư + (x – 2) = -xe-3, > 0.
[10] 1. Solve the first-order equation Tư + (x – 2) = -xe-3, > 0.
(1 point) Find the solution of x2y" + 5xy + (4 + 3x)y = 0, x > 0 of the form Yi = x" Ž Cpx”, n=0 where co = : 1. Enter r = Cn = n = 1,2,3,...
(1 point) Find the solution of xy" + 5xy' + (4 + 1x)y = 0, x > 0 of the form Yi = x n=0 where co = 1. Enter r = -2 Cn = - n= 1,2,3,...
(1 point) Find the solution of x²y" + 5xy' + (4 – 3x) y = 0, x > 0 of the form y=x" Wazek, k=0 where ao = 1. r = help (numbers) ak = , k=1,2,3,... help (formulas)
Find a general solution to the given Cauchy-Euler equation for t> 0. 12d²y dy + 2t- dt - 6y = 0 dt² The general solution is y(t) =
4. At right, the point charges 2 4x are fixed on the y axis Note In this problem, let k 1/4neo a. Show that the magnitude of the resultant electric field at point P can be expressed in the form: Ep (2kg/x2) ( (a2/x2)-5/2 - 1) b. Show that in the case where x >» a the magnitude of resultant electric field at point P can be approximated by Hint: make use of the approximation (1 + α)N is valid...
Find the Laplace Transform of f(t)= - lifts 4; f(t) = 1 if t> 4.
Solve y'' +9y = $(t – 6), y(0) = y'(0) = 0 g(t) = for t < 6 for t > 6
3. [10pts] Consider the DE: xy" + 7xy' + Ty = 0. (a) Find the roots rı and r2 of the indicial equation of the DE (with rı >r2). r = r2 = Solution: (b) If we use Frobenius method to solve the DE, we obtain for the largest indicial root and for n > 0, a recurrence acn relation of the form Cn+1 where a and b are constants. Find a and b. m11
dx Determine x= f(t) for (t? +4t) 4x + 4,t> 0; f(1) = 3. dt For (1? + 4t) dx dt = 4x +4, x= f(t) =
[10] 1. Solve the first-order equation Tư + (x – 2) = -xe-3, > 0.
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