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APM2611 Assignment 4 Memo | Due 24 September 2025. Step-by-Step Calculations provided. Question 1
Use the power series method to solve the initial value problem:
y00 xy0 + 4y = 2, y(0) = 0, y0(0) = 1.
Question 2
Consider the function
f (t) =
8><
>:
sin t 0 t <
sin(t ) t < 2
0 otherwise
.
(2.1) Find the Laplace transform of f (t) by first principles, the table of integrals and
Z b
a
f (t) sin(t ) dt =
Z b
a
f ( + ) sin d .
APM2611 Assignment 4 Memo | Due 24 September 2025. Step-by-Step Calculations provided. Question 1
Use the power series method to solve the initial value problem:
y00 xy0 + 4y = 2, y(0) = 0, y0(0) = 1.
Question 2
Consider the function
f (t) =
8><
>:
sin t 0 t <
sin(t ) t < 2
0 otherwise
.
(2.1) Find the Laplace transform of f (t) by first principles, the table of integrals and
Z b
a
f (t) sin(t ) dt =
Z b
a
f ( + ) sin d .
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APM2611 Assignment 4 Memo | Due 24 September 2025. Step-by-Step Calculations provided. Question 1
Use the power series method to solve the initial value problem:
y00 xy0 + 4y = 2, y(0) = 0, y0(0) = 1.
Question 2
Consider the function
f (t) =
8><
>:
sin t 0 t <
sin(t ) t < 2
0 otherwise
.
(2.1) Find the Laplace transform of f (t) by first principles, the table of integrals and
Z b
a
f (t) sin(t ) dt =
Z b
a
f ( + ) sin d .
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