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Worksheet tackling differential equations using separation of variables.
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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
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