Suppose r1=3+i3, r2=-1. Write the general solution if a)constant coefficents, b) Cauchy-Euler 1/2

Question

Question

Suppose r1=3+i3 1/2 , r2=-1. Write the general solution if a)constant coefficents, b) Cauchy-Euler

math Advanced-Math

Answer 1

Answer #1

Solution: Given that the roots of the characteristic equation are

(a) constant coefficients: Then the general solution is
(b) For Cauchy-Euler. The general solution is

Answer 2

Similar Homework Help Questions

4. a) Find the general solution of the Cauchy-Euler equation 4x3y" - 4x2y"+3xy 0 b) Use...

4. a) Find the general solution of the Cauchy-Euler equation 4x3y" - 4x2y"+3xy 0 b) Use the variation of parameters to find the general solution of 4x3y"-4x2y, + 3x/ = 6x7/2
Use the properties of a Cauchy-Euler system to find a general solution of the given system....

Use the properties of a Cauchy-Euler system to find a general solution of the given system. 3 7 tx'(t)= X(t), t> - 3 13 For t>0, any Cauchy-Euler system of the form tx' = Ax with A an nxn constant matrix has nontrivial solutions of the form x(t)= t'u if and only ifr is an eigenvalue of A and u is a corresponding eigenvector. x(t) = 0
Use the properties of a Cauchy-Euler system to find a general solution of the given system....

Use the properties of a Cauchy-Euler system to find a general solution of the given system. 2 9 tx'(t) X(t), t> 0 -2 13 For t>0, any Cauchy-Euler system of the form tx' = Ax with A an nxn constant matrix has nontrivial solutions of the form x(t) = t’u if and only if ris an eigenvalue of A and u is a corresponding eigenvector. x(t) =

Use the properties of a Cauchy-Euler system to find a general solution of the given system....

Use the properties of a Cauchy-Euler system to find a general solution of the given system. 8 5 tx' (t) = X(t), t> 0 - 8 21 For t>0, any Cauchy-Euler system of the form tx' = Ax with A an nxn constant matrix has nontrivial solutions of the form x(t) = t'u if and only if ris an eigenvalue of A and u is a corresponding eigenvector. X(t) = 0
Use the properties of a Cauchy-Euler system to find a general solution of the given system....

Use the properties of a Cauchy-Euler system to find a general solution of the given system. 8 5 tx' (t) = X(t), t> 0 - 8 21 For t>0, any Cauchy-Euler system of the form tx' = Ax with A an nxn constant matrix has nontrivial solutions of the form x(t) = t'u if and only if ris an eigenvalue of A and u is a corresponding eigenvector. X(t) = 0
The general solution of the Cauchy-Euler differential equation x’y" + 5xy' + 4y = 0 is...

The general solution of the Cauchy-Euler differential equation x’y" + 5xy' + 4y = 0 is a) y = ce-* + c2e-4x b) y = c;e-2x + czxe-2x d) y = Cyx-2 + c2x-2 Inx c) y = C1x-1 + c2x Select one: C a

9. Solve the IVP with Cauchy-Euler ODE: xy"txy+4y-0; y(1)-o, y )--3 = 0 , use Variat...

9. Solve the IVP with Cauchy-Euler ODE: xy"txy+4y-0; y(1)-o, y )--3 = 0 , use Variat 0 10. Given that y = GXtar2 is a solution of the Cauchy-Euler ODE x, "+ 2xy-2 Parameters to find the general solution of the non-homogeneous ODE y+2xy-y homogeneoury"rQ&)e-ar)-
Consider the following tables R1 and R2: R1.A1 R1.B1 ------------ 1 1 NULL 2 3 NULL R2.A2 R2.B2...

Consider the following tables R1 and R2: R1.A1 R1.B1 ------------ 1 1 NULL 2 3 NULL R2.A2 R2.B2 ------------ 1 1 NULL 2 3 NULL The tuple (3, NULL, 3, NULL) appears in the answer of which of the following SQL Statements? Check all that apply A. select * from R1,R2; B. select * from R1,R2 where R1.A1=R2.A2; C. select * from R1,R2 where R1.A1=R2.A2 and R1.B1=R2.B2; Suppose relation R(A,B,C) has the following tuples A B C ----- 2 3 4 5 3 4...
Find the general solution to the homogeneous differential equation d2ydt2−23dydt+130y=0 The solution can be written in the form y=C1er1t+C2er2t with r1<r2 Using this form, r1= and r2=

Find the general solution to the homogeneous differential equationd2ydt2−23dydt+130y=0d2ydt2−23dydt+130y=0The solution can be written in the formy=C1er1t+C2er2ty=C1er1t+C2er2twithr1<r2r1<r2Using this form, r1=r1= and r2=

Suppose you are solving a linear homogenous differential equation. State the general solution for each of...

Suppose you are solving a linear homogenous differential equation. State the general solution for each of the following situations. You may assume that the dependent variable is y, and y = y(t). a. Second-order constant-coefficient equation, with auxiliary equation roots r = -2 +V-49 b. Second-order constant-coefficient equation, with auxiliary equation roots r = -2 + 149 c. Second-order Cauchy-Euler equation, with auxiliary equation roots r = -2 EVO d. Fourth-order constant-coefficient equation, with auxiliary equation roots r = -6,...