Homework Answers
Add Answer to:
4.4: Let 1 0 1 and b(t)- -1 1 0 (a) Find the general real solution of the linear ODE (t) A(t). (b...
Let A = ( a1 0 ... 0 0 a2 ... 0 ... ... ... 0...
Let
A = ( a1 0 ... 0
0 a2 ... 0
... ... ...
0 0 an)
be an n * n matrix, where a1, a2, . . . , an are
nonzero real numbers.
(a) Find the general solution to the system of equations ->
->
x' = A * x
(b) Solve the initial value problem x1(0) =
x2(0) = · · · = xn(0) = k, for some constant
k.
(c) Solve the initial value problem
(x1(0) x2(0)...
5. Repeat the same questions in 4.) for the ODE Py"- tt+2)y+(t+2)y2t3, (t>0) (a) Find the general solution of the homogeneous ODE y"- 5y +6y 0. Particularly find yi and (b) Find the...
5. Repeat the same questions in 4.) for the ODE Py"- tt+2)y+(t+2)y2t3, (t>0) (a) Find the general solution of the homogeneous ODE y"- 5y +6y 0. Particularly find yi and (b) Find the equivalent nonhomogeneous system of first order with the chan of variable y (c) Show that (nvand 2( re solutions of the homogeneous system of ODEs (d) Find the variation of parameters equations that have to be satisfic 1 for y(t) vi(t)u(t) + (e) Find the variation of...
just focus on A,B,D 1. Homogeneous ODE Find a general solution of the linear non-constant coefficient,...
just focus on A,B,D
1. Homogeneous ODE Find a general solution of the linear non-constant coefficient, homogeneous ODE for y(x) x3y'" – 3xy" + (6 – x2)xy' – (6 – x?)y = 0 as follows. a) You are given that yı(x) = x is a solution to the above homogeneous ODE. Confirm (by substitution) that this is the case. b) Apply reduction of order to find the remaining two solutions, then state the general solution. (Hint: The substitution y2(x) =...
1. Let u be a solution of the wave equation u 0. Let the points A, B, C, D be the vertices of the...
1. Let u be a solution of the wave equation u 0. Let the points A, B, C, D be the vertices of the paralleogram formed by the two pairs of characteristic lines r-ctC1,x- ct-2,+ ct- di,r +ct- d2 Show that u (A)+u (C)-u (B) + u (D Use this to find u satisfying For which (x, t) can you determine u (x, t) uniquely this way? 2. Suppose u satisfies the wave equation utt -curr0 in the strip 0...
(1 point) A. Let g(t) be the solution of the initial value problem dy dt with g(1)1 Find g(t) B. Let f(t) be the solution of the initial value problem dy dt with f(0) 0 Find f(t). C. Find a constant...
(1 point) A. Let g(t) be the solution of the initial value problem dy dt with g(1)1 Find g(t) B. Let f(t) be the solution of the initial value problem dy dt with f(0) 0 Find f(t). C. Find a constant c so that solves the differential equation in part B and k(1) 13. cE
(1 point) A. Let g(t) be the solution of the initial value problem dy dt with g(1)1 Find g(t) B. Let f(t) be the solution...
Find a general solution to the given differential equation. 21y'' + 8y' - 5y = 0 A general solution is y(t) = _______ .
1.Find a general solution to the given differential equation. 21y'' + 8y' - 5y = 0 A general solution is y(t) = _______ .2.Solve the given initial value problem. y'' + 3y' = 0; y(0) = 12, y'(0)= - 27 The solution is y(t) = _______ 3.Find three linearly independent solutions of the given third-order differential equation and write a general solution as an arbitrary linear combination of them z"'+z"-21z'-45z = 0 A general solution is z(t) = _______
First-Order ODE (a) .Find the general solution of the following ODE: (b). Find the general...
First-Order ODE
(a) .Find the general solution of the following ODE:
(b). Find the general solution (for x > 0) of the ODE :
Hint: try the change of variables u ≜ x, v ≜ y/x.
(c). Find the solution to the ODE
that satisfies y(2) = 15.
Hint: Try separation of variables. For integration,
try partial fraction decomposition.
2Ꮖy 2 Ꭸ , . + <+5 12 , fi - z - ,fix = zu y' = y2...
For #1 and #2, find the general solution of the ODE system tX' = AX, t>...
For #1 and #2, find the general solution of the ODE system tX' = AX, t> 0. (You do NOT need to verify that the Wronskian is nonzero.) 1. A= ( 1)
homo 2nd order linear equations is necessarily the number -b/2a)]. 1. Find the general solution to...
homo 2nd order linear equations
is necessarily the number -b/2a)]. 1. Find the general solution to the following homogeneous differential equations. (a) y" - 2y + y = 0 (b) 9y" + 6y + y = 0 (c) 4y" + 12y +9y = 0 (d) y' - 6y +9y = 0 2. Solve the the following initial value problems. (a) 9y" - 12y + 4y = 0 with y(0) = 2 and y(0) = -1 (b) y' + 4y +...
(1 point) Consider the initial value problem -51เซี. -4 มี(0) 0 -5 a Find the eigenvalue λ, an eigenvector ul and a gen...
(1 point) Consider the initial value problem -51เซี. -4 มี(0) 0 -5 a Find the eigenvalue λ, an eigenvector ul and a generalized eigenvector u2 for the coefficient matrix of this linear system -5 u2 = b. Find the most general real-valued solution to the linear system of differential equations. Use t as the independent variable in your answers c2 c. Solve the original initial value problem m(t) = 2(t)-
(1 point) Consider the initial value problem -51เซี. -4 มี(0)...
Let
A = ( a1 0 ... 0
0 a2 ... 0
... ... ...
0 0 an)
be an n * n matrix, where a1, a2, . . . , an are
nonzero real numbers.
(a) Find the general solution to the system of equations ->
->
x' = A * x
(b) Solve the initial value problem x1(0) =
x2(0) = · · · = xn(0) = k, for some constant
k.
(c) Solve the initial value problem
(x1(0) x2(0)...
5. Repeat the same questions in 4.) for the ODE Py"- tt+2)y+(t+2)y2t3, (t>0) (a) Find the general solution of the homogeneous ODE y"- 5y +6y 0. Particularly find yi and (b) Find the equivalent nonhomogeneous system of first order with the chan of variable y (c) Show that (nvand 2( re solutions of the homogeneous system of ODEs (d) Find the variation of parameters equations that have to be satisfic 1 for y(t) vi(t)u(t) + (e) Find the variation of...
just focus on A,B,D
1. Homogeneous ODE Find a general solution of the linear non-constant coefficient, homogeneous ODE for y(x) x3y'" – 3xy" + (6 – x2)xy' – (6 – x?)y = 0 as follows. a) You are given that yı(x) = x is a solution to the above homogeneous ODE. Confirm (by substitution) that this is the case. b) Apply reduction of order to find the remaining two solutions, then state the general solution. (Hint: The substitution y2(x) =...
1. Let u be a solution of the wave equation u 0. Let the points A, B, C, D be the vertices of the paralleogram formed by the two pairs of characteristic lines r-ctC1,x- ct-2,+ ct- di,r +ct- d2 Show that u (A)+u (C)-u (B) + u (D Use this to find u satisfying For which (x, t) can you determine u (x, t) uniquely this way? 2. Suppose u satisfies the wave equation utt -curr0 in the strip 0...
(1 point) A. Let g(t) be the solution of the initial value problem dy dt with g(1)1 Find g(t) B. Let f(t) be the solution of the initial value problem dy dt with f(0) 0 Find f(t). C. Find a constant c so that solves the differential equation in part B and k(1) 13. cE
(1 point) A. Let g(t) be the solution of the initial value problem dy dt with g(1)1 Find g(t) B. Let f(t) be the solution...
First-Order ODE
(a) .Find the general solution of the following ODE:
(b). Find the general solution (for x > 0) of the ODE :
Hint: try the change of variables u ≜ x, v ≜ y/x.
(c). Find the solution to the ODE
that satisfies y(2) = 15.
Hint: Try separation of variables. For integration,
try partial fraction decomposition.
2Ꮖy 2 Ꭸ , . + <+5 12 , fi - z - ,fix = zu y' = y2...
For #1 and #2, find the general solution of the ODE system tX' = AX, t> 0. (You do NOT need to verify that the Wronskian is nonzero.) 1. A= ( 1)
homo 2nd order linear equations
is necessarily the number -b/2a)]. 1. Find the general solution to the following homogeneous differential equations. (a) y" - 2y + y = 0 (b) 9y" + 6y + y = 0 (c) 4y" + 12y +9y = 0 (d) y' - 6y +9y = 0 2. Solve the the following initial value problems. (a) 9y" - 12y + 4y = 0 with y(0) = 2 and y(0) = -1 (b) y' + 4y +...
(1 point) Consider the initial value problem -51เซี. -4 มี(0) 0 -5 a Find the eigenvalue λ, an eigenvector ul and a generalized eigenvector u2 for the coefficient matrix of this linear system -5 u2 = b. Find the most general real-valued solution to the linear system of differential equations. Use t as the independent variable in your answers c2 c. Solve the original initial value problem m(t) = 2(t)-
(1 point) Consider the initial value problem -51เซี. -4 มี(0)...
Most questions answered within 3 hours.
-
3) What are the typical social structures in a global city?
asked 1 hour ago -
Luther Corporation
Consolidated Balance Sheet
December 31, 2019 and 2018 (in $ millions)
Assets
2019
2018...
asked 1 hour ago -
(Expected rate of return and risk) Carter Inc. is evaluating a
security. Calculate the investment’s expected...
asked 3 hours ago -
What specific indicators can point to lack of progress for
African Americans in American society?
asked 4 hours ago -
1-The Electrons in a beam are moving at 2.7×108 m/s in an
electric field of 15000...
asked 5 hours ago -
A gas tank is a vertical cylinder. It has a radius of 1m, a
height of...
asked 5 hours ago -
Accent Software faces the following conditions. All of these
support Accent’s use of a market-penetration pricing...
asked 6 hours ago -
A mathematically inclined friend emails you the following
instructions: "Meet me in the cafeteria the first...
asked 6 hours ago -
A monopoly sells in two countries . The demand curves in the two
countries are p1...
asked 7 hours ago -
A .15kg rubber ball is bounced off a wall. Before hitting the
wall, the ball moves...
asked 8 hours ago -
A manufacturing company preparing to build a new plant is
considering three potential locations for it....
asked 8 hours ago -
B. If compound Y has approximately the same values of solubility
in toluene as compound X,...
asked 9 hours ago