Consider the following differential equation for A = 4 and B =
4: y''(t) + Ay'(t) + By(t) = 8u(t) + -6t u(t) where u(t) is the
unit step function. Assume initial conditions: y'(0) = -6 y(0) = 5
Solve this differential equation to obtain an answer of the form
shown below. Enter the value for the coefficient c3. Please enter
your answer as a number in decimal format (not a
fraction).
Homework Answers
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Consider the following differential equation for A = 4 and B =
4: y''(t) + Ay'(t)...
Consider the following differential equation for A = 4 and B = 4: y''(t) + Ay'(t) + By(t) = 1u(t)...
Consider the following differential equation for A = 4 and B =
4: y''(t) + Ay'(t) + By(t) = 1u(t) + -1t u(t) where u(t) is the
unit step function. Assume initial conditions: y'(0) = -4 y(0) = 2
Solve this differential equation to obtain an answer of the form
shown below. Enter the value for the coefficient c3. Please enter
your answer as a number in decimal format (not a
fraction).
y(t) = co0(t) + Ga(t) + c2 ta(t)...
Question 2 (15 points) Solve the differential equation for the general solution y 6y' 73y 0...
Question 2 (15 points) Solve the differential equation for the general solution y 6y' 73y 0 y(t) C cos(3t) C2 sin(3t) y(t) = C1 cos(8t) + C2 sin(8t) y(t) cos(8t) +C2e" sin(St) y(t) Ce cos(8t) Cest sin (8t) y (t) = Cleft cos (8t) + C2eft sin (8t) (t)Cest cos(9)Cesin (9t) Previous Page Next Page Page 2 of9
Solve the differential equation S-20x by the method of y- 24 d, Solve the differential equation...
Solve the differential equation S-20x by the method of y- 24 d, Solve the differential equation y" +z/aAc' by the equation yy- b, c. 2。メsolve the differential equation 144y"-ay'+y-12(x+r) by the nl21)by the method of undetermnined coefficients. y(12 12 d. yr(G+Ga)e1/12: + 288 + 12x + 12 e12 Solve the differential equation "19dy-sin 14x by the method of undeternined coefficient a. cos 14x+ 14C2 sin 14x
Find the general solution of the differential equation by using the system of linear equation. pl...
find the general solution of the differential equation by using the system of linear equation. please need to be solve by differential equation expert. d^2x/dt^2+x+4dy/dt-4y=4e^t , dx/dt-x+dy/dt+9y=0 Its answer will look lile that: x(t)= c1 e^-2t (2sin(t)+cos(t))+ c2 e^-2t (4e^t-3sin(t)-4cos(t))+ 20 c3 e^-2t(e^t-sin(t)-cos(t))+2 e^t, y(t)= c1 e^-2t sin(t)+ c2 e^-2t(e^t-2sin(t)-cos(t))+ c3 e^-2t(5e^t-12sin(t)-4cos(t))
1. Consider the Partial Differential Equation ot u(0,t) = u(r, t) = 0 a(x, 0)-x (Y), sin (! We know the general solution to the Basic Heat Equation is u(z,t)-Σ b e ). n= 1 (b) Find the unique solutio...
1. Consider the Partial Differential Equation ot u(0,t) = u(r, t) = 0 a(x, 0)-x (Y), sin (! We know the general solution to the Basic Heat Equation is u(z,t)-Σ b e ). n= 1 (b) Find the unique solution that satisfies the given initial condition ur, 0) -2. (Hint: bn is given by the Fourier Coefficients-f(z),sin(Y- UsefulFormulas/Facts for PDEs/Fourier Series 1)2 (TiT) » x sin aL(1)1 a24(부) (TiT) 1)+1 0
1. Consider the Partial Differential Equation ot u(0,t) =...
Problem 1 (20 points) Consider the differential equation for the function y given by 4 cos(4y)...
Problem 1 (20 points) Consider the differential equation for the function y given by 4 cos(4y) 40e 2e) cos(8t)+5 eu 2t) sin(8t)/ - 12e - 0. 8 sin(4y) y a. (4/20) Just by reordering terms on the left hand side above, write the equation as Ny + M 0 for appropriate functions N, M. Then compute: aN(t, y) ayM(t, y) b. (8/20) Find an integrating factor If you keep an integrating constant, call it c (t) N and M M,...
Determine the form of a particular solution for the differential equation. Do not solve. y" -...
Determine the form of a particular solution for the differential equation. Do not solve. y" - 4y' + 5y = e 7 + t sin 6t - cos 6t The form of a particular solution is yp(t)- (Do not use d, D, e, E, I, or I as arbitrary constants since these letters already have defined meanings.)
Use the method of variation of parameters to determine the general solution of the given differential equation. y(4)+2y′′+y=3sin(t) Use C1, C2, C3, ... for the constants of integration. Enclose argume...
Use the method of variation of parameters to determine the general solution of the given differential equation. y(4)+2y′′+y=3sin(t) Use C1, C2, C3, ... for the constants of integration. Enclose arguments of functions in parentheses. For example, sin(2x). y(t)=
a. Find a particular solution to the nonhomogeneous differential equation y" + 16y = cos(4x) +...
a. Find a particular solution to the nonhomogeneous differential equation y" + 16y = cos(4x) + sin(4x). Yo = (xsin(4x))/8-(xcos(4x))/8 help (formulas) b. Find the most general solution to the associated homogeneous differential equation. Use ci and C2 in your answer to denote arbitrary constants. Enter c1 as c1 and C2 as c2. Un = c1cos(4x)+c2sin(4x) help (formulas) c. Find the solution to the original nonhomogeneous differential equation satisfying the initial conditions y(0) = 3 and y'(0) = 2. y...
2. For this differential equation y"(t) - 6y'(t) + 15y(t) = 2r(t), determine (4 points) a)...
2. For this differential equation y"(t) - 6y'(t) + 15y(t) = 2r(t), determine (4 points) a) Transfer function b) The poles and zeros of the transfer function c) Given that r(t) = sin(3t),y(0) = -1, y'(0) = -4, find y(t) using partial fraction expansion
Consider the following differential equation for A = 4 and B =
4: y''(t) + Ay'(t) + By(t) = 1u(t) + -1t u(t) where u(t) is the
unit step function. Assume initial conditions: y'(0) = -4 y(0) = 2
Solve this differential equation to obtain an answer of the form
shown below. Enter the value for the coefficient c3. Please enter
your answer as a number in decimal format (not a
fraction).
y(t) = co0(t) + Ga(t) + c2 ta(t)...
Question 2 (15 points) Solve the differential equation for the general solution y 6y' 73y 0 y(t) C cos(3t) C2 sin(3t) y(t) = C1 cos(8t) + C2 sin(8t) y(t) cos(8t) +C2e" sin(St) y(t) Ce cos(8t) Cest sin (8t) y (t) = Cleft cos (8t) + C2eft sin (8t) (t)Cest cos(9)Cesin (9t) Previous Page Next Page Page 2 of9
Solve the differential equation S-20x by the method of y- 24 d, Solve the differential equation y" +z/aAc' by the equation yy- b, c. 2。メsolve the differential equation 144y"-ay'+y-12(x+r) by the nl21)by the method of undetermnined coefficients. y(12 12 d. yr(G+Ga)e1/12: + 288 + 12x + 12 e12 Solve the differential equation "19dy-sin 14x by the method of undeternined coefficient a. cos 14x+ 14C2 sin 14x
1. Consider the Partial Differential Equation ot u(0,t) = u(r, t) = 0 a(x, 0)-x (Y), sin (! We know the general solution to the Basic Heat Equation is u(z,t)-Σ b e ). n= 1 (b) Find the unique solution that satisfies the given initial condition ur, 0) -2. (Hint: bn is given by the Fourier Coefficients-f(z),sin(Y- UsefulFormulas/Facts for PDEs/Fourier Series 1)2 (TiT) » x sin aL(1)1 a24(부) (TiT) 1)+1 0
1. Consider the Partial Differential Equation ot u(0,t) =...
Problem 1 (20 points) Consider the differential equation for the function y given by 4 cos(4y) 40e 2e) cos(8t)+5 eu 2t) sin(8t)/ - 12e - 0. 8 sin(4y) y a. (4/20) Just by reordering terms on the left hand side above, write the equation as Ny + M 0 for appropriate functions N, M. Then compute: aN(t, y) ayM(t, y) b. (8/20) Find an integrating factor If you keep an integrating constant, call it c (t) N and M M,...
Determine the form of a particular solution for the differential equation. Do not solve. y" - 4y' + 5y = e 7 + t sin 6t - cos 6t The form of a particular solution is yp(t)- (Do not use d, D, e, E, I, or I as arbitrary constants since these letters already have defined meanings.)
a. Find a particular solution to the nonhomogeneous differential equation y" + 16y = cos(4x) + sin(4x). Yo = (xsin(4x))/8-(xcos(4x))/8 help (formulas) b. Find the most general solution to the associated homogeneous differential equation. Use ci and C2 in your answer to denote arbitrary constants. Enter c1 as c1 and C2 as c2. Un = c1cos(4x)+c2sin(4x) help (formulas) c. Find the solution to the original nonhomogeneous differential equation satisfying the initial conditions y(0) = 3 and y'(0) = 2. y...
2. For this differential equation y"(t) - 6y'(t) + 15y(t) = 2r(t), determine (4 points) a) Transfer function b) The poles and zeros of the transfer function c) Given that r(t) = sin(3t),y(0) = -1, y'(0) = -4, find y(t) using partial fraction expansion
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