(1 point) Solve the following
initial value problem: (3y2−t2y5)dydt+t2y4=0, y(1)=3. y(t)=
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(1 point) Solve the following
initial value problem: (3y2−t2y5)dydt+t2y4=0, y(1)=3. y(t)=
(1 point) Solve the following...
(1 point) Solve the initial value problem 2yy' 3 = y 3x with y(0) = 9...
(1 point) Solve the initial value problem 2yy' 3 = y 3x with y(0) = 9 a. To solve this, we should use the substitution y^2 help (formulas) With this substitution, help (formulas) y' = help (formulas) Enter derivatives using prime notation (e.g., you would enter y' for b. After the substitution from the previous part, we obtain the following linear differential equation in x, u, u'. help (equations) c. The solution to the original initial value problem is described...
3) Solve the following initial value problem. ( 1; 0 <t y" + y = f(t),...
3) Solve the following initial value problem. ( 1; 0 <t y" + y = f(t), y(0) = 2, y'(0) = -1, where f(t) = } nere -1; En VI t
(1 point) Solve the following initial value problem: y" + 9y = u5(t); y(0) = 0,...
(1 point) Solve the following initial value problem: y" + 9y = u5(t); y(0) = 0, y' (O) = 0. For step functions, remember to use uſt - c) rather than uc(t). g(t) = ||
(1 point) Consider the initial value problem my" cy' +ky = F(t), y(0) = 0, y'(0) = 0 modeling the motion of...
(1 point) Consider the initial value problem my" cy' +ky = F(t), y(0) = 0, y'(0) = 0 modeling the motion of a spring-mass-dashpot system initially at rest and subjected to an applied force F(t), where the unit of force is the Newton (N). Assume that m 2 kilograms, 8 kilograms per second, k = 80 Newtons per meter, and the applied force in Newtons is c if 0tT/2, if t > /2 40 F(t)= a. Solve the initial value...
(1 point) Consider the initial value problem my"+cy'+ky F(t), y(0) = 0, y'(0) = 0 modeling...
(1 point) Consider the initial value problem my"+cy'+ky F(t), y(0) = 0, y'(0) = 0 modeling the motion of a spring-mass-dashpot system initially at rest and subjected to an applied force F(), where the unit of force is the Newton (N). Assume that m 2 kilograms, c 8 kilograms per second, k 80 Newtons per meter, and F(t) 60 cos(8t) Newtons. a. Solve the initial value problem. help (formulas) b. Determine the long-term behavior of the system. Is lim y(t)=...
1 point) Consider the initial value problem my" +cy' + ky-F(t), y' (0)-0 y(0)-0, modeling the...
1 point) Consider the initial value problem my" +cy' + ky-F(t), y' (0)-0 y(0)-0, modeling the motion of a spring-mass-dashpot system initially at rest and subjected to an applied force F(t), where the unit of force is the Newton (N) Assume that m = 2 kilograms, C-8 kilograms per second, k-80 Newtons per meter, and F(t) = 40 sin(6) Newtons. a. Solve the initial value problem. y0) help (formulas) b. Determine the long-term behavior of the system. ls lim y()...
(1 point) Consider the initial value problem y"36y g(t), y(0) 0, /(0) 0, t if 0<t<5 0 if 5t<00. where g(t)...
(1 point) Consider the initial value problem y"36y g(t), y(0) 0, /(0) 0, t if 0<t<5 0 if 5t<00. where g(t) create the corresponding algebraic equation. Denote the Laplace transform of y(t) by Y(s). Do not move any terms from a. Take the Laplace transform of both sides the given differential equation one side of the equation the other (until you get to part (b) below). help (formulas) b. Solve your equation for Y(s). Y(s) C{y(t)} solve for y(t) c....
(1 point) Consider the initial value problem y" + 4y = 8t, y(0) =3, y'(0) =...
(1 point) Consider the initial value problem y" + 4y = 8t, y(0) =3, y'(0) = 4. a. Take the Laplace transform of both sides of the given differential equation to create the corresponding algebraic equation. Denote the Laplace transform of y(t) by Y(s). Do not move any terms from one side of the equation to the other (until you get to part (b) below). 8/s^2 help (formulas) b. Solve your equation for Y(s). Y(s) = L{y(t)} = c. Take...
1. For the initial value problem y' = 3y2/3, y(2) = 0, there is a trivial...
1. For the initial value problem y' = 3y2/3, y(2) = 0, there is a trivial solution, y(x) = 0. Find a nontrivial solution to this IVP. Does this contradict the existence theory for solutions of first onder IVPs y = f(x, y), y(x) = yo? Briefly explain. (VALUE: 4 l ations:
1 point) Consider the initial value problem my "tou' + ky-F(t), y(0)-0, y"(0)-0 modeling the motion...
1 point) Consider the initial value problem my "tou' + ky-F(t), y(0)-0, y"(0)-0 modeling the motion of a spring-mass-dashpot system initially at rest and subjected to an applied force F(t), where the unit of force is the Newton (N). Assume that m-2 kilograms, c-8 kilograms per second, k 80 Newtons per meter, and the applied force in Newtons is 50 if0 st/2, F(t) = if t > π/2. a Solve the initial value problem, using that the displacement y(t) and...
(1 point) Solve the initial value problem 2yy' 3 = y 3x with y(0) = 9 a. To solve this, we should use the substitution y^2 help (formulas) With this substitution, help (formulas) y' = help (formulas) Enter derivatives using prime notation (e.g., you would enter y' for b. After the substitution from the previous part, we obtain the following linear differential equation in x, u, u'. help (equations) c. The solution to the original initial value problem is described...
3) Solve the following initial value problem. ( 1; 0 <t y" + y = f(t), y(0) = 2, y'(0) = -1, where f(t) = } nere -1; En VI t
(1 point) Solve the following initial value problem: y" + 9y = u5(t); y(0) = 0, y' (O) = 0. For step functions, remember to use uſt - c) rather than uc(t). g(t) = ||
(1 point) Consider the initial value problem my" cy' +ky = F(t), y(0) = 0, y'(0) = 0 modeling the motion of a spring-mass-dashpot system initially at rest and subjected to an applied force F(t), where the unit of force is the Newton (N). Assume that m 2 kilograms, 8 kilograms per second, k = 80 Newtons per meter, and the applied force in Newtons is c if 0tT/2, if t > /2 40 F(t)= a. Solve the initial value...
(1 point) Consider the initial value problem my"+cy'+ky F(t), y(0) = 0, y'(0) = 0 modeling the motion of a spring-mass-dashpot system initially at rest and subjected to an applied force F(), where the unit of force is the Newton (N). Assume that m 2 kilograms, c 8 kilograms per second, k 80 Newtons per meter, and F(t) 60 cos(8t) Newtons. a. Solve the initial value problem. help (formulas) b. Determine the long-term behavior of the system. Is lim y(t)=...
1 point) Consider the initial value problem my" +cy' + ky-F(t), y' (0)-0 y(0)-0, modeling the motion of a spring-mass-dashpot system initially at rest and subjected to an applied force F(t), where the unit of force is the Newton (N) Assume that m = 2 kilograms, C-8 kilograms per second, k-80 Newtons per meter, and F(t) = 40 sin(6) Newtons. a. Solve the initial value problem. y0) help (formulas) b. Determine the long-term behavior of the system. ls lim y()...
(1 point) Consider the initial value problem y"36y g(t), y(0) 0, /(0) 0, t if 0<t<5 0 if 5t<00. where g(t) create the corresponding algebraic equation. Denote the Laplace transform of y(t) by Y(s). Do not move any terms from a. Take the Laplace transform of both sides the given differential equation one side of the equation the other (until you get to part (b) below). help (formulas) b. Solve your equation for Y(s). Y(s) C{y(t)} solve for y(t) c....
(1 point) Consider the initial value problem y" + 4y = 8t, y(0) =3, y'(0) = 4. a. Take the Laplace transform of both sides of the given differential equation to create the corresponding algebraic equation. Denote the Laplace transform of y(t) by Y(s). Do not move any terms from one side of the equation to the other (until you get to part (b) below). 8/s^2 help (formulas) b. Solve your equation for Y(s). Y(s) = L{y(t)} = c. Take...
1. For the initial value problem y' = 3y2/3, y(2) = 0, there is a trivial solution, y(x) = 0. Find a nontrivial solution to this IVP. Does this contradict the existence theory for solutions of first onder IVPs y = f(x, y), y(x) = yo? Briefly explain. (VALUE: 4 l ations:
1 point) Consider the initial value problem my "tou' + ky-F(t), y(0)-0, y"(0)-0 modeling the motion of a spring-mass-dashpot system initially at rest and subjected to an applied force F(t), where the unit of force is the Newton (N). Assume that m-2 kilograms, c-8 kilograms per second, k 80 Newtons per meter, and the applied force in Newtons is 50 if0 st/2, F(t) = if t > π/2. a Solve the initial value problem, using that the displacement y(t) and...
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