Find the general solution of the following system of differential Equations. Show all the steps of...
Solve the Differential problem?
Find the general solution of the following system of differential Equations. Show a" the steps of your work. y = 6 yı - y2 V2 = 5y +442 Page 1 a + (hp)
please answer all the following quesitons and show all
working
1. Find the general solution to the following homogeneous differential equations. y" - 2y' + y = 0 (b) 9y" + 6y' + y = 0 4y' +12y +9y=0 (d) y" - 6y' +9y = 0
1. Find the general solution to the next system of differential
equations.
2. Find the general solution of the following system of
differential equations by parametric conversion.
Y' = [2 =3] [2 – 4) (1-3 y+ 2t2 + 10+] t2 +9t +3 Sa = - 3x+y+3t ly' = 27 - 4y+et
Undetermined Coefficients: Find the general solution for the
differential equations.
Find the general solution for the following differential equations. (1) y' - y" – 4y' + 4y = 5 - e* + e-* (2) y" + 2y' + y = x²e- (3) y" - 4y' + 8y = x3; y(0) = 2, y'(0) = 4
Please show solutions.
Answer:
1. Find a general solution to the following differential equations: (a) y" + y = 0 (b) y" – 2y' + 264 = 0 (c) 4x²y" – 3y = 0 (d) y" + 4y = 9 sin(t). (e) y" – 6y' + 9y = 6e3x 1. (a) y = ci + c2e- (b) y = cle' cos(5t) + czet sin(5t) (c) y = cit-1/2 + c2t3/2 (d) y = ci cos(2t) + c2 sin(2t) + 3...
1. Find the general solution for each of the following differential equations (10 points each): y" - 2y - 3y = 32 y" - y' - 2y = -2 + 4.2 y" + y' - 6y = 12e3+ + 12e-2x y" - 2y - 3y = 3.re* y" + 2y + y = 2e-* (Hint: you'll use Rule 7. at least once)
Find the general solution to the system of linear differential equations X'=AX. The independent variable is t. The eigenvalues and the corresponding eigenvectors are provided for you. x1' = 12x1 - 8x2 x2 = -4X1 + 8x2 The eigenvalues are 11 = 16 and 12 = 4 . The corresponding eigenvectors are: K1 = K2= Step 1. Find the nonsingular matrix P that diagonalizes A, and find the diagonal matrix D: p = 11 Step 2. Find the general solution...
2. Differential equations and direction fields (a) Find the general solution to the differential equation y' = 20e3+ + + (b) Find the particular solution to the initial value problem y' = 64 – 102, y(0) = 11. (e) List the equilibrium solutions of the differential equation V = (y2 - 1) arctan() (d) List all equilibrium solutions of the differential equation, and classify the stability of each: V = y(y - 6)(n-10) (e) Use equilibrium solutions and stability analysis...
Find the general solutions of the given differential system of
equations using whichever method seems appropriate.
3.1' + 2.1 + y - 6y = 5e, 4.x' + 2.1 + y - 8y = 5e + 2t – 3
Problem 2. (10pts.) Find the general solution to the system of differential equations y' = 2 - 2 z' = 5y + 42