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(1 point) In this exercise you will solve the initial value problem e-9 y" – 184'...
(8 pts) In this problem you will solve the non-homogeneous differential equation y" + 9y =...
(8 pts) In this problem you will solve the non-homogeneous differential equation y" + 9y = sec (3x) (1) Let C and C2 be arbitrary constants. The general solution to the related homogeneous differential equation y" + 9y = 0 is the function yn (x) = C1 yı(2) + C2 y2(x) = C1 +C2 NOTE: The order in which you enter the answers is important; that is, Cif(x) + C2g(x) + C19(x) + C2 f(x). (2) The particular solution yp(x)...
(1 point) a. Find a particular solution to the nonhomogeneous differential equation y" + 3y -...
(1 point) a. Find a particular solution to the nonhomogeneous differential equation y" + 3y - 10y = ex. yp = help (formulas) b. Find the most general solution to the associated homogeneous differential equation. Use cy and c2 in your answer to denote arbitrary constants, and enter them as c1 and c2. Yh = help (formulas) c. Find the most general solution to the original nonhomogeneous differential equation. Use cy and C2 in your answer to denote arbitrary constants....
(1 point) In this exercise you will solve the initial value problem 1 +x2' (1) Let Ci and C2 be a...
(1 point) In this exercise you will solve the initial value problem 1 +x2' (1) Let Ci and C2 be arbitrary constants. The general solution to the related homogeneous differential equation " - 4y+4y 0 is the function C2 NOTE: The order in which you enter the answers is important, that is, CJU) + Gg(x)ヂGg(x) + CN 2) The particular solution yo(x) to the differential equation y" +4ys of the form yo) -yi) u)x) and (x) = 2x (3) The...
(1 point) Solve y" + 2y' + 2y = 4te* cos(t). 1) Solve the homogeneous part:...
(1 point) Solve y" + 2y' + 2y = 4te* cos(t). 1) Solve the homogeneous part: y" + 2y' + 2y = 0 for Yh, using a real basis. Note the coded answer is ordered. If your basis is correct and your answer is not accepted, try again with the other ordering. Yn = C1 te^(-+)*cost +C2 te^(-t)*cost 2) Compute the particular solution y, via complexifying the differential equation: Note that the forcing et cos(t) = Re(el-1+i)t). You will solve...
(1 point) Solve y" + 2y + 2y = 4te-t cos(t). 1) Solve the homogeneous part:...
(1 point) Solve y" + 2y + 2y = 4te-t cos(t). 1) Solve the homogeneous part: y' + 2y + 2y = 0 for Yh, using a real basis. Note the coded answer is ordered. If your basis is correct and your answer is not accepted, try again with the other ordering. Yn = C1 e^(-t)sin(t) +C2 e^(-t)cos(t) . 2) Compute the particular solution yp via complexifying the differential equation: Note that the forcing e * cos(t) = Re(el 1+i)t)....
(1 point) Solve the following differential equation by variation of parameters. Fully evaluate all integrals. y"...
(1 point) Solve the following differential equation by variation of parameters. Fully evaluate all integrals. y" +9y sec(3x) a. Find the most general solution to the associated homogeneous differential equation. Use c1 and c2 in your answer to denote arbitrary constants, and enter them as ct and c2. help (formulas) b. Find a particular solution to the nonhomogeneous differential equation y" +9y sec(3x). yp elp (formulaS c. Find the most general solution to the original nonhomogeneous differential equation. Use c...
(1 point) Consider the initial value problem -2 j' = [ y, y(0) +3] 0 -2...
(1 point) Consider the initial value problem -2 j' = [ y, y(0) +3] 0 -2 a. Find the eigenvalue 1, an eigenvector 1, and a generalized eigenvector ū2 for the coefficient matrix of this linear system. = --1 V2 = b. Find the most general real-valued solution to the linear system of differential equations. Use t as the independent variable in your answers. g(t) = C1 + C2 c. Solve the original initial value problem. yı(t) = y2(t) ==
Consider the differential equation e24 y" – 4y +4y= t> 0. t2 (a) Find T1, T2,...
Consider the differential equation e24 y" – 4y +4y= t> 0. t2 (a) Find T1, T2, roots of the characteristic polynomial of the equation above. 11,12 M (b) Find a set of real-valued fundamental solutions to the homogeneous differential equation corresponding to the one above. yı(t) M y2(t) = M (C) Find the Wronskian of the fundamental solutions you found in part (b). W(t) M (d) Use the fundamental solutions you found in (b) to find functions ui and Usuch...
Consider the ODE below. y' + 364 = sec(62) Find the general solution to the associated...
Consider the ODE below. y' + 364 = sec(62) Find the general solution to the associated homogeneous equation. Use C1 and C2 as arbitrary constants. y(2) Use variation of parameters to find a particular solution to the nonhomogeneous equation. State the two functions vi and U2 produced by the system of equations. Let vi be the function containing a trig function and V, be the function that does not contain a trig function. You may omit absolute value signs and...
Find the solution y of the initial value problem 3"(t) = 2 (3(t). y(1) = 0,...
Find the solution y of the initial value problem 3"(t) = 2 (3(t). y(1) = 0, y' (1) = 1. +3 g(t) = M Solve the initial value problem g(t) g” (t) + 50g (+)? = 0, y(0) = 1, y'(0) = 7. g(t) = Σ Use the reduction order method to find a second solution ya to the differential equation ty" + 12ty' +28 y = 0. knowing that the function yı(t) = + 4 is solution to that...
(8 pts) In this problem you will solve the non-homogeneous differential equation y" + 9y = sec (3x) (1) Let C and C2 be arbitrary constants. The general solution to the related homogeneous differential equation y" + 9y = 0 is the function yn (x) = C1 yı(2) + C2 y2(x) = C1 +C2 NOTE: The order in which you enter the answers is important; that is, Cif(x) + C2g(x) + C19(x) + C2 f(x). (2) The particular solution yp(x)...
(1 point) a. Find a particular solution to the nonhomogeneous differential equation y" + 3y - 10y = ex. yp = help (formulas) b. Find the most general solution to the associated homogeneous differential equation. Use cy and c2 in your answer to denote arbitrary constants, and enter them as c1 and c2. Yh = help (formulas) c. Find the most general solution to the original nonhomogeneous differential equation. Use cy and C2 in your answer to denote arbitrary constants....
(1 point) In this exercise you will solve the initial value problem 1 +x2' (1) Let Ci and C2 be arbitrary constants. The general solution to the related homogeneous differential equation " - 4y+4y 0 is the function C2 NOTE: The order in which you enter the answers is important, that is, CJU) + Gg(x)ヂGg(x) + CN 2) The particular solution yo(x) to the differential equation y" +4ys of the form yo) -yi) u)x) and (x) = 2x (3) The...
(1 point) Solve y" + 2y' + 2y = 4te* cos(t). 1) Solve the homogeneous part: y" + 2y' + 2y = 0 for Yh, using a real basis. Note the coded answer is ordered. If your basis is correct and your answer is not accepted, try again with the other ordering. Yn = C1 te^(-+)*cost +C2 te^(-t)*cost 2) Compute the particular solution y, via complexifying the differential equation: Note that the forcing et cos(t) = Re(el-1+i)t). You will solve...
(1 point) Solve y" + 2y + 2y = 4te-t cos(t). 1) Solve the homogeneous part: y' + 2y + 2y = 0 for Yh, using a real basis. Note the coded answer is ordered. If your basis is correct and your answer is not accepted, try again with the other ordering. Yn = C1 e^(-t)sin(t) +C2 e^(-t)cos(t) . 2) Compute the particular solution yp via complexifying the differential equation: Note that the forcing e * cos(t) = Re(el 1+i)t)....
(1 point) Solve the following differential equation by variation of parameters. Fully evaluate all integrals. y" +9y sec(3x) a. Find the most general solution to the associated homogeneous differential equation. Use c1 and c2 in your answer to denote arbitrary constants, and enter them as ct and c2. help (formulas) b. Find a particular solution to the nonhomogeneous differential equation y" +9y sec(3x). yp elp (formulaS c. Find the most general solution to the original nonhomogeneous differential equation. Use c...
(1 point) Consider the initial value problem -2 j' = [ y, y(0) +3] 0 -2 a. Find the eigenvalue 1, an eigenvector 1, and a generalized eigenvector ū2 for the coefficient matrix of this linear system. = --1 V2 = b. Find the most general real-valued solution to the linear system of differential equations. Use t as the independent variable in your answers. g(t) = C1 + C2 c. Solve the original initial value problem. yı(t) = y2(t) ==
Consider the differential equation e24 y" – 4y +4y= t> 0. t2 (a) Find T1, T2, roots of the characteristic polynomial of the equation above. 11,12 M (b) Find a set of real-valued fundamental solutions to the homogeneous differential equation corresponding to the one above. yı(t) M y2(t) = M (C) Find the Wronskian of the fundamental solutions you found in part (b). W(t) M (d) Use the fundamental solutions you found in (b) to find functions ui and Usuch...
Consider the ODE below. y' + 364 = sec(62) Find the general solution to the associated homogeneous equation. Use C1 and C2 as arbitrary constants. y(2) Use variation of parameters to find a particular solution to the nonhomogeneous equation. State the two functions vi and U2 produced by the system of equations. Let vi be the function containing a trig function and V, be the function that does not contain a trig function. You may omit absolute value signs and...
Find the solution y of the initial value problem 3"(t) = 2 (3(t). y(1) = 0, y' (1) = 1. +3 g(t) = M Solve the initial value problem g(t) g” (t) + 50g (+)? = 0, y(0) = 1, y'(0) = 7. g(t) = Σ Use the reduction order method to find a second solution ya to the differential equation ty" + 12ty' +28 y = 0. knowing that the function yı(t) = + 4 is solution to that...
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