[SOLVED] AMS361-Homework 1

Description

Problem 1.1 : Verify by substitution whether the given functions are solutions of the given DE. Primes denote derivatives with respect to 𝑥.

𝑦^′′ + 𝑦′ = sin 20𝑥 ;  𝑦₁ = cos 𝑥 + sin 𝑥 , 𝑦₂ = cos 20𝑥 + sin 𝑥 , 𝑦₃ = cos𝑥 + sin 20𝑥

Problem 1.2 Verify that  satisfies the given DE and then determine a value of the constant 𝐶 so that 𝑦 satisfies the given initial condition (IC).

𝑦^′ − 7𝑥⁶𝑦 = 0;     𝑦 ,             𝑦(0) = 2020

Problem 1.3 Find the PS of the IVP:

𝑦^′ sin 𝑥 + 𝑦 cos𝑥 = 0

{

𝑦(𝜋/2) = 2020

Problem 1.4 Solve the following IVP. 𝑥

𝑦𝜋

Problem 1.5 Find the GS of the DE (Primes denote derivatives WRT 𝑥):

𝑦′ = (𝑥𝑦′ + 𝑦)𝑦²⁰²⁰ Hint: Recall relationship 𝑦^′ = ^𝑑𝑦 = (^𝑑𝑥)⁻¹ and regard 𝑥 as DV and 𝑦 as IV. 𝑑𝑥 𝑑𝑦