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II. Answer the following questions concerning the simultaneous differential equa- dac tions below. Here, à dt...
Here is the phase portrait of a homogeneous linear system of differential tions. 4. equa- (a) Cla...
Here is the phase portrait of a homogeneous linear system of differential tions. 4. equa- (a) Classify the equilibrium (b) If λί is the eigenvalue with corresponding eigenvector (1,1) and A2 is the eigenvalue with corresponding eigenvector (-1,3), place the three numbers 0, λ, and λ2 in order frorn least to greatest. (c) If ((t), y(t) is the solution satisfying the initial condition (x(0),y(0)- (-2,2). Find i. lim r(t) i. lim rlt) ii. lim y(t) iv. lim y(t)
Here is...
(6). The quantities x(t) and y(t) satisfy the simultaneous equations dt dt dx dt where x(0)-y(0)-...
(6). The quantities x(t) and y(t) satisfy the simultaneous equations dt dt dx dt where x(0)-y(0)-ay (0)-0, and ax (0)-λ. Here n, μ, and λ are all positive real numbers. This problem involves Laplace transforms, has three parts, and is continued on the next page. You must use Laplace transforms where instructed to receive credit for your solution (a). Define the Laplace Transforms X(s) -|e"x(t)dt and Y(s) -e-"y(t)dt Laplace Transform the differential equations for x(t) and y(t) above, and incorporate...
QUESTION 1 (15 MARKS) a) Given 4'{+93}=LC }-( - siu (au) sin’au) sin(2t - 2u) du....
QUESTION 1 (15 MARKS) a) Given 4'{+93}=LC }-( - siu (au) sin’au) sin(2t - 2u) du. Use the convolution theorem to determine the value of constant a. (5 marks) b) Using Laplace transform, solve the simultaneous differential equations dac dt - 4 =1+t, +2=t-1. dt given that x(0) = 0 and y(0) = 3. (10 marks)
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)...
The following system of differential equations has a repeated eigenvalue 2 da dt 2x3y dy 2y...
The following system of differential equations has a repeated eigenvalue 2 da dt 2x3y dy 2y dt Suppose we choose its corresponding eigenvector to be (-1, 0). The initial conditions are x(0) = 5.77 and y(0)= 1.99 Find the value of x(0.31), giving your answer to 3 decimal places
Here are the question and answer of ordinary differential equation. Please show the steps. Thanks! 5....
Here are the question and answer of ordinary differential
equation.
Please show the steps. Thanks!
5. (a) Show that yo-Vi and y(t)-1/1 are solutions of the differential equa- tion (*) 21%y+3 ty' - y=0 on the interval 0<t<0. (6) Compute W[ 2](). What happens as i approaches zero? (c) Show that y(i) and yz(1) form a fundamental set of solutions of (*) on the interval 0<t<0. (d) Solve the initial-value problem 21%y" +3 ty'-y 0; y(1)-2, y'(l)-1. 5. (b) W=32;...
7. Solve the following differential equations. dy 2 y= 5x, x>0. + a) dx dx 1+2x 4e', t>0 b) t dt 7....
7. Solve the following differential equations. dy 2 y= 5x, x>0. + a) dx dx 1+2x 4e', t>0 b) t dt
7. Solve the following differential equations. dy 2 y= 5x, x>0. + a) dx dx 1+2x 4e', t>0 b) t dt
Differential Equations Need Help! Will Rate! Question 1 (35) 1. Build the characteristic polynomial for the DE z',-4x,-52-0 and find two particular solutions. Here, x' = dx/dt, x" = d2x/dt...
Differential Equations Need Help! Will Rate!
Question 1 (35) 1. Build the characteristic polynomial for the DE z',-4x,-52-0 and find two particular solutions. Here, x' = dx/dt, x" = d2x/dt2. (15) 2. Verify that the two solutions are linearly independent. (5) 3. Build the general solution to the DE as a linear combination of these two solutions. (5) 4. Using the general solution, calculate the solution for the same DE with the initial conditions z(0) 5, x(0) 3. (10) Question...
3. Consider the following stiff system of autonomous ordinary differential equations du f(u, u) =-3u +3,...
3. Consider the following stiff system of autonomous ordinary differential equations du f(u, u) =-3u +3, u(0)2 = ' dt de g(u, v) -2000u - 1000, v(0)-3 Note that 1 u<2 and -4 <v < 3 for all t. (a) Find the Jacobian matrix for the system of equa tions (b) Find the eigenvalues of the Jacobian matrix. (c) In the figure the shaded region shows the region of absolute stability, in the complex h plane, for third order explicit...
Please answer the following questions that a person new to this course would be able to...
Please answer the following questions that a person new to this
course would be able to understand.( Include theorem.)
Problem 6: Consider the linear systems of differential equations a) Sketch the direction Seld for the line gystem. write StreamPlotl(x-2y, 2x-3y] İn Wolframı Alpha a) Use the method of elimination to find a second order linear differential equation that is satisfied by (t b) Find particular solutions x(t) and y(t) such that x(0) 1 and y(0) 2
Here is the phase portrait of a homogeneous linear system of differential tions. 4. equa- (a) Classify the equilibrium (b) If λί is the eigenvalue with corresponding eigenvector (1,1) and A2 is the eigenvalue with corresponding eigenvector (-1,3), place the three numbers 0, λ, and λ2 in order frorn least to greatest. (c) If ((t), y(t) is the solution satisfying the initial condition (x(0),y(0)- (-2,2). Find i. lim r(t) i. lim rlt) ii. lim y(t) iv. lim y(t)
Here is...
(6). The quantities x(t) and y(t) satisfy the simultaneous equations dt dt dx dt where x(0)-y(0)-ay (0)-0, and ax (0)-λ. Here n, μ, and λ are all positive real numbers. This problem involves Laplace transforms, has three parts, and is continued on the next page. You must use Laplace transforms where instructed to receive credit for your solution (a). Define the Laplace Transforms X(s) -|e"x(t)dt and Y(s) -e-"y(t)dt Laplace Transform the differential equations for x(t) and y(t) above, and incorporate...
QUESTION 1 (15 MARKS) a) Given 4'{+93}=LC }-( - siu (au) sin’au) sin(2t - 2u) du. Use the convolution theorem to determine the value of constant a. (5 marks) b) Using Laplace transform, solve the simultaneous differential equations dac dt - 4 =1+t, +2=t-1. dt given that x(0) = 0 and y(0) = 3. (10 marks)
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)...
The following system of differential equations has a repeated eigenvalue 2 da dt 2x3y dy 2y dt Suppose we choose its corresponding eigenvector to be (-1, 0). The initial conditions are x(0) = 5.77 and y(0)= 1.99 Find the value of x(0.31), giving your answer to 3 decimal places
Here are the question and answer of ordinary differential
equation.
Please show the steps. Thanks!
5. (a) Show that yo-Vi and y(t)-1/1 are solutions of the differential equa- tion (*) 21%y+3 ty' - y=0 on the interval 0<t<0. (6) Compute W[ 2](). What happens as i approaches zero? (c) Show that y(i) and yz(1) form a fundamental set of solutions of (*) on the interval 0<t<0. (d) Solve the initial-value problem 21%y" +3 ty'-y 0; y(1)-2, y'(l)-1. 5. (b) W=32;...
7. Solve the following differential equations. dy 2 y= 5x, x>0. + a) dx dx 1+2x 4e', t>0 b) t dt
7. Solve the following differential equations. dy 2 y= 5x, x>0. + a) dx dx 1+2x 4e', t>0 b) t dt
Differential Equations Need Help! Will Rate!
Question 1 (35) 1. Build the characteristic polynomial for the DE z',-4x,-52-0 and find two particular solutions. Here, x' = dx/dt, x" = d2x/dt2. (15) 2. Verify that the two solutions are linearly independent. (5) 3. Build the general solution to the DE as a linear combination of these two solutions. (5) 4. Using the general solution, calculate the solution for the same DE with the initial conditions z(0) 5, x(0) 3. (10) Question...
3. Consider the following stiff system of autonomous ordinary differential equations du f(u, u) =-3u +3, u(0)2 = ' dt de g(u, v) -2000u - 1000, v(0)-3 Note that 1 u<2 and -4 <v < 3 for all t. (a) Find the Jacobian matrix for the system of equa tions (b) Find the eigenvalues of the Jacobian matrix. (c) In the figure the shaded region shows the region of absolute stability, in the complex h plane, for third order explicit...
Please answer the following questions that a person new to this
course would be able to understand.( Include theorem.)
Problem 6: Consider the linear systems of differential equations a) Sketch the direction Seld for the line gystem. write StreamPlotl(x-2y, 2x-3y] İn Wolframı Alpha a) Use the method of elimination to find a second order linear differential equation that is satisfied by (t b) Find particular solutions x(t) and y(t) such that x(0) 1 and y(0) 2
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