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2.7. Consider the differential equation for the RC circuit in Fig. P.2.12: Figure P. 2.12 R=1...
2.14. For each differential equation given below, find the solution for t 2 0 with the...
2.14. For each differential equation given below, find the solution for t 2 0 with the specified input signal and subject to the specified initial value. Use the general solution technique outlined in Section 2.5.4. of y (t) dt2 dy (t) dy (t) , た0 dy (t) dt22 t 4-t2 + 3 y (t)-x(t) , dP2+3y(t) =x(t), x(t)=u(t), y(0) = 2 dt22+2dy(2+y(t)=x(t) , x(t) = e-2t u (t), x (t) = (t+ 1) u (t) , y (0)--2 dy (t)...
(15 points) In this problem we consider an equation in differential form M dx + N...
(15 points) In this problem we consider an equation in differential form M dx + N dy = 0. (- (4xy2 + 4y)) dx +(- (4x²y + 4x))dy = 0 Find My N. If the problem is exact find a function F(x, y) whose differential, dF(x, y) is the left hand side of the differential equation. That is, level curves F(t, y) = C, give implicit general solutions to the differential equation. If the equation is not exact, enter NE...
Consider the differential equation dy dt = t - 2 According to the differential equation, what...
Consider the differential equation dy dt = t - 2 According to the differential equation, what is the value of y (0)? Question 3 Consider the differential equation dy dt = t - 2 and the given information y(0) = 1. Select the figure that shows the correct graphical representation of y' (O). 0 O 3 y 21 + -2 y 2 1 2 1 2 A z -1 O 3 y 2 X 2. z -1 O 3 2+...
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...
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))
+ co BY Draw Erase 4 QUESTION 3 Consider the following differential equation + 4y =...
+ co BY Draw Erase 4 QUESTION 3 Consider the following differential equation + 4y = 6e with initial conditions when x = 0, y = -2 and = 8 (a) Use the technique of Laplace transformation to find L) (10 marks) (b) Consider the cover-up rule to simplify your expression for Lly) and use the table below to obtain L"? (y) to find the final solution y for the above differential equation (15 marks) A short table of Laplace...
mat lab only Osts 10 Problem 3 Numerically integrate the 2nd order linear differential equation on...
mat lab only
Osts 10 Problem 3 Numerically integrate the 2nd order linear differential equation on the interval +5 + 4y - 0 v0-0 0-6 y(t) - 2e" - 2e-41 and compare it to the solution a) Plot the numerical solution and the true solution for y(t) (20 pts) b) Plot the numerical solution and the true solution for dy/dt (10 pts)
1. Consider the differential equation" = y2 - 4y - 5. a) Find any equilibrium solution(s)....
1. Consider the differential equation" = y2 - 4y - 5. a) Find any equilibrium solution(s). b) Create an appropriate table of values and then sketch (using the grid provided) a direction field for this differential equation on OSIS 3. Be sure to label values on your axes. c) Using the direction field, describe in detail the behavior of y ast approaches infinity. 2. Short answer: State whether or not the differential equation is linear. If it is linear, state...
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...
R wW L Consider the electric circuit in the figure above. This circuit is described by...
R wW L Consider the electric circuit in the figure above. This circuit is described by the system of differential equations d dt RC Suppose that R = 1 ohms, C= 5 farads, and L 20 henrys. Suppose also that i (0) 2 amperes and v (0) 36 volts. Find i (t) and v (t). Click here to enter or edit your answer i(t) The solution is given by v(t) Click if vou would like to Show Work for this...
2.14. For each differential equation given below, find the solution for t 2 0 with the specified input signal and subject to the specified initial value. Use the general solution technique outlined in Section 2.5.4. of y (t) dt2 dy (t) dy (t) , た0 dy (t) dt22 t 4-t2 + 3 y (t)-x(t) , dP2+3y(t) =x(t), x(t)=u(t), y(0) = 2 dt22+2dy(2+y(t)=x(t) , x(t) = e-2t u (t), x (t) = (t+ 1) u (t) , y (0)--2 dy (t)...
(15 points) In this problem we consider an equation in differential form M dx + N dy = 0. (- (4xy2 + 4y)) dx +(- (4x²y + 4x))dy = 0 Find My N. If the problem is exact find a function F(x, y) whose differential, dF(x, y) is the left hand side of the differential equation. That is, level curves F(t, y) = C, give implicit general solutions to the differential equation. If the equation is not exact, enter NE...
Consider the differential equation dy dt = t - 2 According to the differential equation, what is the value of y (0)? Question 3 Consider the differential equation dy dt = t - 2 and the given information y(0) = 1. Select the figure that shows the correct graphical representation of y' (O). 0 O 3 y 21 + -2 y 2 1 2 1 2 A z -1 O 3 y 2 X 2. z -1 O 3 2+...
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...
+ co BY Draw Erase 4 QUESTION 3 Consider the following differential equation + 4y = 6e with initial conditions when x = 0, y = -2 and = 8 (a) Use the technique of Laplace transformation to find L) (10 marks) (b) Consider the cover-up rule to simplify your expression for Lly) and use the table below to obtain L"? (y) to find the final solution y for the above differential equation (15 marks) A short table of Laplace...
mat lab only
Osts 10 Problem 3 Numerically integrate the 2nd order linear differential equation on the interval +5 + 4y - 0 v0-0 0-6 y(t) - 2e" - 2e-41 and compare it to the solution a) Plot the numerical solution and the true solution for y(t) (20 pts) b) Plot the numerical solution and the true solution for dy/dt (10 pts)
1. Consider the differential equation" = y2 - 4y - 5. a) Find any equilibrium solution(s). b) Create an appropriate table of values and then sketch (using the grid provided) a direction field for this differential equation on OSIS 3. Be sure to label values on your axes. c) Using the direction field, describe in detail the behavior of y ast approaches infinity. 2. Short answer: State whether or not the differential equation is linear. If it is linear, state...
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...
R wW L Consider the electric circuit in the figure above. This circuit is described by the system of differential equations d dt RC Suppose that R = 1 ohms, C= 5 farads, and L 20 henrys. Suppose also that i (0) 2 amperes and v (0) 36 volts. Find i (t) and v (t). Click here to enter or edit your answer i(t) The solution is given by v(t) Click if vou would like to Show Work for this...
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