Calculus HW

Miran Anwar, mth 235 ss21 1: Hw10-3.2-LT-IVP. Due: 04/26/2021 at 11:00pm EDT.

See in LN, § 3.2, See Example 3.2.2. 1. (10 points)

Consider the initial value problem for function y given by,

y′′−2 y′−3 y = 0, y(0) =−3, y′(0) = 5.

Part 1: Finding Y (s) (a) Find the Laplace Transform of the solution, Y (s) = L

[ y(t)

] .

Y (s) =

Note: We are not asking for the solution y(t), but for the Laplace Transform of the solution, Y (s). Part 2: Rewriting Y (s) Part 3: Finding y(t)

See in LN, § 3.2, See Example 3.2.2. 2. (10 points)

Consider the initial value problem for function y given by,

y′′−6 y′+ 13 y = 0, y(0) =−3, y′(0) =−5.

Part 1: Finding Y (s) (a) Find the Laplace Transform of the solution, Y (s) = L

[ y(t)

] .

Y (s) =

Note: We are not asking for the solution y(t), but for the Laplace Transform of the solution, Y (s).

Part 2: Rewriting Y (s) Part 3: Finding y(t)

See in LN, § 3.2, See Example 3.2.3. 3. (10 points)

Consider the initial value problem for function y given by,

y′′−4 y′+ 4 y = 0, y(0) =−5, y′(0) =−3.

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Part 1: Finding Y (s) (a) Find the Laplace Transform of the solution, Y (s) = L

[ y(t)

] .

Y (s) =

Note: We are not asking for the solution y(t), but for the Laplace Transform of the solution, Y (s).

Part 2: Rewriting Y (s) Part 3: Finding y(t)

See in LN, § 3.2, See Example 3.2.4. 4. (10 points)

Consider the initial value problem for function y given by,

y′′+ y′−6 y = et, y(0) = 0, y′(0) = 0.

Part 1: Finding Y (s) (a) Find the Laplace Transform of the solution, Y (s) = L

[ y(t)

] .

Y (s) =

Note: We are not asking for the solution y(t), but for the Laplace Transform of the solution, Y (s).

Part 2: Rewriting Y (s) Part 3: Finding y(t)

See in LN, § 3.2, See Example 3.2.5. 5. (10 points)

Consider the initial value problem for function y given by,

y′′−5 y′+ 4 y = 3 cos(5t), y(0) = 5, y′(0) = 4.

Part 1: Finding Y (s) (a) Find the Laplace Transform of the solution, Y (s) = L

[ y(t)

] .

Y (s) =

Note: We are not asking for the solution y(t), but for the Laplace Transform of the solution, Y (s).

Part 2: Rewriting Y (s) Part 3: Finding y(t)

2

See in LN, § 3.2, See Example 3.2.4. 6. (10 points)

Consider the initial value problem for function y given by,

y′′−4 y′−5 y = 2, y(0) = 0, y′(0) = 0.

Part 1: Finding Y (s) (a) Find the Laplace Transform of the solution, Y (s) = L

[ y(t)

] .

Y (s) =

Note: We are not asking for the solution y(t), but for the Laplace Transform of the solution, Y (s).

Part 2: Rewriting Y (s) Part 3: Finding y(t)

See in LN, § 3.2, See Example 3.2.2. 7. (0 points)

Consider the initial value problem for function y given by,

y′′−5 y′+ 4 y = 0, y(0) =−1, y′(0) = 2.

Part 1: Finding Y (s) (a) Find the Laplace Transform of the solution, Y (s) = L

[ y(t)

] .

Y (s) =

Note: We are not asking for the solution y(t), but for the Laplace Transform of the solution, Y (s).

Part 2: Rewriting Y (s) Part 3: Finding y(t)

See in LN, § 3.2, See Example 3.2.2. 8. (0 points)

Consider the initial value problem for function y given by,

y′′+ 6 y′+ 34 y = 0, y(0) =−5, y′(0) = 1.

3

Part 1: Finding Y (s) (a) Find the Laplace Transform of the solution, Y (s) = L

[ y(t)

] .

Y (s) =

Note: We are not asking for the solution y(t), but for the Laplace Transform of the solution, Y (s).

Part 2: Rewriting Y (s) Part 3: Finding y(t)

See in LN, § 3.2, See Example 3.2.3. 9. (0 points)

Consider the initial value problem for function y given by,

y′′+ 2 y′+ 1 y = 0, y(0) = 3, y′(0) =−1.

Part 1: Finding Y (s) (a) Find the Laplace Transform of the solution, Y (s) = L

[ y(t)

] .

Y (s) =

Note: We are not asking for the solution y(t), but for the Laplace Transform of the solution, Y (s).

Part 2: Rewriting Y (s) Part 3: Finding y(t)

See in LN, § 3.2, See Example 3.2.5. 10. (0 points)

Consider the initial value problem for function y given by,

y′′−4 y′+ 3 y =−4 sin(4t), y(0) = 5, y′(0) =−2.

Part 1: Finding Y (s) (a) Find the Laplace Transform of the solution, Y (s) = L

[ y(t)

] .

Y (s) =

Note: We are not asking for the solution y(t), but for the Laplace Transform of the solution, Y (s).

Part 2: Rewriting Y (s) Part 3: Finding y(t)

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