Pure 2.7 - Methods in Differential Equations

Question 1

How would you solve a first-order differential equation of the form (d𝑦/d𝑥)+P(𝑥)𝑦=Q(𝑥)?

Answer 1

By multiplying every term by the integrating factor e^(∫P(𝑥)d𝑥).

Question 2

What is a second-order homogeneous differential equation?

Answer 2

A linear differential equation of the form 𝑎(d²𝑦/d𝑥²)+𝑏(d𝑦/d𝑥)+𝑐𝑦=0