Assignment 01 Answers
Year 2025
0027 63 985 5033
,
, QUESTION 1
𝑑𝑦 𝑦 𝑦
− ( ) = 2( )
𝑑𝑥 𝑥 𝑥
This is a separable differential equation
𝑑𝑦 𝑦 𝑦
− ( ) = 2( )
𝑑𝑥 𝑥 𝑥
𝑑𝑦 𝑦
= 3( )
𝑑𝑥 𝑥
𝑑𝑦 1
∫ = ∫ 𝑑𝑥
3𝑦 𝑥
1 1 1
∫ 𝑑𝑦 = ∫ 𝑑𝑥
3 𝑦 𝑥
1
ln|𝑦| = ln|𝑥| + ln |𝑐|
3
1
ln |𝑦|3 = ln |𝑥𝑐|
1
𝑒 ln |𝑦|3 = 𝑒 ln |𝑥𝑐|
1
𝑦 3 = 𝑥𝑐
𝒚 = 𝒄𝟏 𝒙𝟑 𝒘𝒉𝒆𝒓𝒆 𝒄𝟏 = 𝒄𝟑