[Q.8, 7 pts each] Solve the system of ODEs 22+1+t [Q.8, 7 pts each] Solve the system of ODEs 22+1+t
Simulink problems System of ODES Solve the system of ODEs with a suitable Simulink system. Graphically compare the Simulink solutions with the exact solutions (symbolic solution). y'1 (t) = -3y1(t) – 2y2(t), y1(0) = 1, y'2 (t) = 4y1(t) + 2y2(t), y2(0) = 1. Upload your Simulink model and MATLAB code with graphical output (LiveScript exported to PDF).
Please solve this problem by hand calculation. Thanks
Consider the following system of two ODES: dx = x-yt dt dy = t+ y from t=0 to t = 1.2 with x(0) = 1, and y(0) = 1 dt (a) Solve with Euler's explicit method using h = 0.4 (b) Solve with the classical fourth-order Runge-Kutta method using h = 0.4. The a solution of the system is x = 4et- 12et- t2 - 3t - 3, y= 2et- t-1. In...
#7 (50 pts) Use an appropriate method to solve the given system 1 8 X'= +
Consider the RLC circuit where R = 5, C = 1, L = 4 and V = 8. 1. Use circuit analysis laws to show that the resistor's voltage and induc- tor's voltage can be modelled as the system of ODEs し」L 2. Solve the eigenvalues and eigenvectors of the coefficient matrix in the system of ODEs. 3. Verify your answer for question (2) by using the eig function in MAT- LAB (make sure you comment on whether your solutions...
Problem 1. (15 points) Solve the following system of ODEs using your Euler implementation and ode45 and compare the errors at the final step. Use h 0.1 and 10 steps. What is the exact solution? Problem 2. (15 points) Express the following differential equation as a system of first order ODEs. Identify all critical points and identify their stability.
Problem 1. (15 points) Solve the following system of ODEs using your Euler implementation and ode45 and compare the errors at...
The step size is actually 0.075 not 0.25. Thanks!
Required information Solve a system of ODEs using Euler's method. Consider the following pair of ODEs over the interval from t= 0 to 0.4 using a step size of 0.25. The initial conditions are 10) = 2 and Z(O) = 4. dy dt = -2y + 4et dz yz? = 32 dt Use the Euler method and write a program to solve this. You do not need to submit the program....
8 H 2 Q iL Vs (t 22 1. vs (t) 2 V; this is a dc source. Solve using a simple circuit analysis method 2. Us (t) 2u (t) V; solve by writing and solving the differential equation for the circuit, as in Ch. 8. You = = 0 for t0. can assume that ir 2u (t) V; solve using the Thévenin method, as in Ch. 8. You can assume that i, = 0 for t< 0. 3. vg...
(1 point) Solving a system of linear ODEs with constant coefficients: Consider the system of equations x' = 3x – 2y y = 4x – 3y = -5x + 4y + 2z, with initial conditions x(0) = 1, y(0) = 2, 2(0) = 0. The matrix of the system is 13 -20 A= | 4 -3 0 1-5 4 2) and defining the column vector r(t) X(t) = y(t) z(t) we get that X' = AX, where X(0 = 2...
hy are they of salt y (t) and y (t) in T and T , respectively.
1212 T2 1. Each of two tanks contain 24 litres of water in which
initially 8 kg (tank 1) and 36 kg (tank 2) of nutrient are
dissolved. The inflow, circulation, and outflow are shown below.
Stirring keeps the mixtures in each tank uniform.
Please EXPLAIN how the equations are formed not just posting
them or I will report.
1. Each of two tanks...
Consider the system of linear ODES 1 (1) = 35 yj (1) - 16 y2 (1) – 26 yz (1), dy2 (1) = 30 yy (0) - 15 y2 (1) – 22 yz (1). di Y3 (1) = 36 y1 (1) - 16 yz (1) - 27 y3 (). (71 The system of equation written as y' (t) = Ay(t), where y(t) = 2(1) (a) Enter the matrix A in the box below. ab sin(a) f a 2 (-1) (-2)(-1...