APM2611 ASSIGNMENT 4 2025 – STEP-BY-STEP CALCULATIONS PROVIDED (DUE 24 SEPTEMBER 2025)

Description

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 .