Homework Answers
This is a linear differential equation. We solve it by multiplying a function called integrating factor through out the differential equation. Then the LHS of the differential equation can be represented as the derivative of product of two functions.
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In each of Problems 6 through 10, solve the initial value problem. 6. y +3y=5e2x –...
Problem 1: Solve the initial value problems: a 2y" – 3y' +y=0 y(0) = 2, 7(0)...
Problem 1: Solve the initial value problems: a 2y" – 3y' +y=0 y(0) = 2, 7(0) = 1 by' + y - 6y = 0 y(0) = -1, y'(0) = 2 cy' + 4y + 3y = 0 y(0) = 1, y'(0) = 0 Problem 2: Solve the initial value problems: a y' +9y = 0 y(0) = 1. 1'(0) = -1 by" - 4y + 13y = 0 y(0) = 1, y'(0) = 3 cy" + ly + ly...
[10] 2. Solve the initial value problem (x² + 3y² + x)y' + 2xy + y...
[10] 2. Solve the initial value problem (x² + 3y² + x)y' + 2xy + y = 0, y(1) = 1.
#6 Solve the initial value problem y(0)- 2, y,(0) 1 y"-3y' + 2y-6(t-3);
#6 Solve the initial value problem y(0)- 2, y,(0) 1 y"-3y' + 2y-6(t-3);
(10 pts) Solve the initial value problem by Laplace transform: y" – 4y + 3y =...
(10 pts) Solve the initial value problem by Laplace transform: y" – 4y + 3y = ezt, y(0) = 0, y'(0) = 0.
[10] 2. Solve the initial value problem (x^ + 3y^ + c)2 + 2xy + y...
[10] 2. Solve the initial value problem (x^ + 3y^ + c)2 + 2xy + y = 0, g(1) = 1.
Solve the initial value problem. y'" – 3y" - y' + 3y = 0; y(0)=5, y'0)...
Solve the initial value problem. y'" – 3y" - y' + 3y = 0; y(0)=5, y'0) = -3. y'(0)=5 The solution is y(t) =
2) Use Laplace Transforms to solve the initial value problem y/ -3y = -10(1-2) with y(0)...
2) Use Laplace Transforms to solve the initial value problem y/ -3y = -10(1-2) with y(0) = 8/9.
6(10pt). Solve the initial value problem ry' + 3y = 2", y(2) = 1.
6(10pt). Solve the initial value problem ry' + 3y = 2", y(2) = 1.
Solve the initial value problem y" + 3y' + 2y = 8(t – 3), y(0) =...
Solve the initial value problem y" + 3y' + 2y = 8(t – 3), y(0) = 2, y'(0) = -2. Answer: y = u3(t) e-(-3) - u3(t)e-2(1-3) + 2e-, y(t) ={ 2e-, t<3, -e-24+6 +2e-l, t>3. 5. [18pt] b) Solve the initial value problem y' (t) = cost + Laplace transforms. +5° 867). cos (t – 7)ds, y(0) – 1 by means of Answer:
Solve the initial-value problem. a) y', _ y'-12y = 0, y(0) = 3, y'(0) = 5 b) y"-4y'+3y 9x2 +4, y(...
Solve the initial-value problem. a) y', _ y'-12y = 0, y(0) = 3, y'(0) = 5 b) y"-4y'+3y 9x2 +4, y(0)-6, y(0) 8
Solve the initial-value problem. a) y', _ y'-12y = 0, y(0) = 3, y'(0) = 5 b) y"-4y'+3y 9x2 +4, y(0)-6, y(0) 8
Problem 1: Solve the initial value problems: a 2y" – 3y' +y=0 y(0) = 2, 7(0) = 1 by' + y - 6y = 0 y(0) = -1, y'(0) = 2 cy' + 4y + 3y = 0 y(0) = 1, y'(0) = 0 Problem 2: Solve the initial value problems: a y' +9y = 0 y(0) = 1. 1'(0) = -1 by" - 4y + 13y = 0 y(0) = 1, y'(0) = 3 cy" + ly + ly...
[10] 2. Solve the initial value problem (x² + 3y² + x)y' + 2xy + y = 0, y(1) = 1.
#6 Solve the initial value problem y(0)- 2, y,(0) 1 y"-3y' + 2y-6(t-3);
(10 pts) Solve the initial value problem by Laplace transform: y" – 4y + 3y = ezt, y(0) = 0, y'(0) = 0.
[10] 2. Solve the initial value problem (x^ + 3y^ + c)2 + 2xy + y = 0, g(1) = 1.
Solve the initial value problem. y'" – 3y" - y' + 3y = 0; y(0)=5, y'0) = -3. y'(0)=5 The solution is y(t) =
2) Use Laplace Transforms to solve the initial value problem y/ -3y = -10(1-2) with y(0) = 8/9.
6(10pt). Solve the initial value problem ry' + 3y = 2", y(2) = 1.
Solve the initial value problem y" + 3y' + 2y = 8(t – 3), y(0) = 2, y'(0) = -2. Answer: y = u3(t) e-(-3) - u3(t)e-2(1-3) + 2e-, y(t) ={ 2e-, t<3, -e-24+6 +2e-l, t>3. 5. [18pt] b) Solve the initial value problem y' (t) = cost + Laplace transforms. +5° 867). cos (t – 7)ds, y(0) – 1 by means of Answer:
Solve the initial-value problem. a) y', _ y'-12y = 0, y(0) = 3, y'(0) = 5 b) y"-4y'+3y 9x2 +4, y(0)-6, y(0) 8
Solve the initial-value problem. a) y', _ y'-12y = 0, y(0) = 3, y'(0) = 5 b) y"-4y'+3y 9x2 +4, y(0)-6, y(0) 8
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