Q1: Solve the following Differential Equations: a) *** - 3y , initial condition y = 2,x= -3 (15 points) b) xer+ y = 0 inition condition, y = 1 when x = 0 (15points) c) + y = ex (15Points)
3. Solve the system of equations 5x + 3y + z 23 3x + 4y-z 21 4x + 5y 2z 26 4. Solve the system of equations. 4x-2y + 3z 27 5x 7y + 4z 39
(differential equations). solve as Bernoulli Equation.
Solve as Bernoulli Ean. y'+3y=y"
Find general solutions of the differential equations to x. 14. xy ry-уз 15. y +3y 3xe3 16. y 2-2xy y2 18. 2x2y-rly,-: уз 20. xy' +3y 3x-3/2 11. x2ys xy + 3y2 25. 2y + (x +1)y'-3x +3
Question 3 Consider the following linear system of differential equations dx: = 2x-3y dt dy dt (a) Write this system of differential equations in matrix form (b) Find the general solution of the system (c) Solve the initial value problem given (0) 3 and y(0)-4 (d) Verify the calculations with MATLAB
Question 3 Consider the following linear system of differential equations dx: = 2x-3y dt dy dt (a) Write this system of differential equations in matrix form (b) Find the...
Q4-Given the following system of equations x-y-z = 6 3x – 3y - 3z = 18 6x – 6y - 6z = 108 How many solution you have in this system? Explain?
Please name technique used to
solve.
Differential Equations Solve: xy" + y = 3y'
Solve the systems of equations by substitution #11 2x-y-2 3x+4y-6 Solve each system by elimination or by any convenient method #13 a) 3x+4y-1 2x-3y-12 b) -4x+3y--!5 3x-2y-4
10. Solve the system of differential equations by using eigenvalues and eigenvectors. x1 = 3x, + 2x2 + 2xz x2 = x + 4x2 + x3 X;' =-2x, - 4x2 – x3
7. Solve the system of equations: ii) X - 3 Y = 2 X - Y = -2 Y= x - 1 X + Y = 11 iii) 2 X. +3Y=2 X - 2Y = 8