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Consider the differential equation y" – 7y + 12 y = 0. (a) Find r1, 72,...
Consider the differential equation y" + 8y' + 15 y=0. (a) Find r1 r2, roots of...
Consider the differential equation y" + 8y' + 15 y=0. (a) Find r1 r2, roots of the characteristic polynomial of the equation above. = 11, 12 M (b) Find a set of real-valued fundamental solutions to the differential equation above. yı(t) M y2(t) M (C) Find the solution y of the the differential equation above that satisfies the initial conditions y(0) = 4, y(0) = -3. g(t) = M (10 points) Solve the initial value problem y" - 54' +...
onsider the differential equation y" - 7y + 12 y = 3 cos(3t). (a) Find r....
onsider the differential equation y" - 7y + 12 y = 3 cos(3t). (a) Find r. 12. roots of the characteristic polynomial of the equation above. ri, r2 = 3,4 (b) Find a set of real-valued fundamental solutions to the homogeneous differential equation corresponding to the one above. Yi (t) = 0 (31) »2(t) = 0 (41) (c) Find a particular solution y, of the differential equation above. y,(t) = Consider the differential equation y! -8y + 15 y =...
Consider the differential equation y" – 7 ý + 12 y = 3 e21. (a) Find...
Consider the differential equation y" – 7 ý + 12 y = 3 e21. (a) Find r1, r2, roots of the characteristic polynomial of the equation above. W r1, r2 = 3,4 (b) Find a set of real-valued fundamental solutions to the homogeneous differential equation corresponding to the one above. yı(t) = e^(3t) M y2(t) = e^(41) (c) Find a particular solution Yp of the differential equation above. M yp(t) = Note: You can earn partial credit on this problem.
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 differential equation (a) Find ri, r2, roots of the characteristic polynomial of the equation...
Consider the differential equation (a) Find ri, r2, roots of the characteristic polynomial of the equation above. T1,T2 (b) Find a set of real-valued fundamental solutions to the homogeneous differential equation corresponding to the one above. n(t) = v2(t) (c) Find a particular solution yp of the differential equation above. Bplt)
Consider the differential equation, L[y] = y'' + p(t)y' + q(t)y = 0, (1) whose coefficients...
Consider the differential
equation, L[y] = y'' + p(t)y' + q(t)y = 0, (1) whose coefficients p
and q are continuous on some open interval I. Choose some point t0
in I. Let y1 be the solution of equation (1) that also satisfies
the initial conditions y(t0) = 1, y'(t0) = 0, and let y2 be the
solution of equation (1) that satisfies the initial conditions
y(t0) = 0, y'(t0) = 1. Then y1 and y2 form a fundamental set...
Consider the BVP for the function y given by 21T (a) Find ri, r2, roots of the characteristic pol...
Consider the BVP for the function y given by 21T (a) Find ri, r2, roots of the characteristic polynomial of the equation above. (b) Find a set of real-valued fundamental solutions to the differential equation above. y (x)-| 3cos(5x) y2 (x)-| 3/5cos(5x)+ksin(5x) (c) Find all solutions y of the boundary value problem. y(r)3cos(5x)+3/5sin(5x) Note 1: If there are no solutions, type No Solution. Note 2: If there are infinitely many solutions, use k for the arbitrary constant.
Consider the BVP...
2. Consider the differential equation ty" – (t+1)y' +y = 2t2 t>0. (a) Check that yı...
2. Consider the differential equation ty" – (t+1)y' +y = 2t2 t>0. (a) Check that yı = et and y2 = t+1 are a fundamental set of solutions to the associated homogeneous equation. (b) Find a particular solution using variation of parameters.
An object of mass 3 grams is attached to a vertical spring with spring constant 27...
An object of mass 3 grams is attached to a vertical spring with spring constant 27 grams/seca. Neglect any friction with the air. (a) Find the differential equation y = fly, y) satisfied by the function y, the displacement of the object from its equilibrium position, positive downwards. Write y for y(t) and yp for y' (t). y = (b) Find rı,r2, roots of the characteristic polynomial of the equation above. ru,r2 = (b) Find a set of real-valued fundamental...
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...
Consider the differential equation y" + 8y' + 15 y=0. (a) Find r1 r2, roots of the characteristic polynomial of the equation above. = 11, 12 M (b) Find a set of real-valued fundamental solutions to the differential equation above. yı(t) M y2(t) M (C) Find the solution y of the the differential equation above that satisfies the initial conditions y(0) = 4, y(0) = -3. g(t) = M (10 points) Solve the initial value problem y" - 54' +...
onsider the differential equation y" - 7y + 12 y = 3 cos(3t). (a) Find r. 12. roots of the characteristic polynomial of the equation above. ri, r2 = 3,4 (b) Find a set of real-valued fundamental solutions to the homogeneous differential equation corresponding to the one above. Yi (t) = 0 (31) »2(t) = 0 (41) (c) Find a particular solution y, of the differential equation above. y,(t) = Consider the differential equation y! -8y + 15 y =...
Consider the differential equation y" – 7 ý + 12 y = 3 e21. (a) Find r1, r2, roots of the characteristic polynomial of the equation above. W r1, r2 = 3,4 (b) Find a set of real-valued fundamental solutions to the homogeneous differential equation corresponding to the one above. yı(t) = e^(3t) M y2(t) = e^(41) (c) Find a particular solution Yp of the differential equation above. M yp(t) = Note: You can earn partial credit on this problem.
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 differential equation (a) Find ri, r2, roots of the characteristic polynomial of the equation above. T1,T2 (b) Find a set of real-valued fundamental solutions to the homogeneous differential equation corresponding to the one above. n(t) = v2(t) (c) Find a particular solution yp of the differential equation above. Bplt)
Consider the differential
equation, L[y] = y'' + p(t)y' + q(t)y = 0, (1) whose coefficients p
and q are continuous on some open interval I. Choose some point t0
in I. Let y1 be the solution of equation (1) that also satisfies
the initial conditions y(t0) = 1, y'(t0) = 0, and let y2 be the
solution of equation (1) that satisfies the initial conditions
y(t0) = 0, y'(t0) = 1. Then y1 and y2 form a fundamental set...
Consider the BVP for the function y given by 21T (a) Find ri, r2, roots of the characteristic polynomial of the equation above. (b) Find a set of real-valued fundamental solutions to the differential equation above. y (x)-| 3cos(5x) y2 (x)-| 3/5cos(5x)+ksin(5x) (c) Find all solutions y of the boundary value problem. y(r)3cos(5x)+3/5sin(5x) Note 1: If there are no solutions, type No Solution. Note 2: If there are infinitely many solutions, use k for the arbitrary constant.
Consider the BVP...
2. Consider the differential equation ty" – (t+1)y' +y = 2t2 t>0. (a) Check that yı = et and y2 = t+1 are a fundamental set of solutions to the associated homogeneous equation. (b) Find a particular solution using variation of parameters.
An object of mass 3 grams is attached to a vertical spring with spring constant 27 grams/seca. Neglect any friction with the air. (a) Find the differential equation y = fly, y) satisfied by the function y, the displacement of the object from its equilibrium position, positive downwards. Write y for y(t) and yp for y' (t). y = (b) Find rı,r2, roots of the characteristic polynomial of the equation above. ru,r2 = (b) Find a set of real-valued fundamental...
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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