Worksheet – Differential Equations using Separation of Variables

1) Find the general solution of the following differential equation:

a) 𝑑𝑦

𝑑𝑥 = 𝑥 + 2𝑥2

b) 𝑑𝑦

𝑑𝑥 = 𝑦

c) 𝑑𝑦

𝑑𝑥 = sin 2𝑥 sec 3𝑦

d) tan 𝑦 𝑑𝑦

𝑑𝑥=

1

(𝑥−1)(𝑥−2)

2) Solve the following differential equations:

a) 𝑑𝑦

𝑑𝑥 = 5𝑥2𝑦3, 𝑦 = 1 when 𝑥 = 0

b) cot 𝑥

sin 𝑦

𝑑𝑦

𝑑𝑥 = 3, 𝑦 =

𝜋

2 when 𝑥 = 0

c) 𝑒𝑥+𝑦 𝑑𝑦𝑑𝑥

= sin 𝑥 , 𝑦 = 0 when 𝑥 = 0