1st-Order Separable DE

𝑃(𝑦, 𝑑𝑦) = 𝑄(𝑥, 𝑑𝑥) # 𝑒.𝑔. 𝑦’ = 𝑥/𝑦

1st-Order Homogenous DE

𝑦’ = 𝐹(𝑦/𝑥) # 𝑒.𝑔. 𝑦’ = (𝑥² + 𝑦²)/𝑥𝑦

1^st-Order Bernoulli DE

𝑦’ + 𝑃(𝑥)𝑦 = 𝑄(𝑥)𝑦^𝑛 # 𝑛∉{0,1}

1st-Order Exact DE

𝑃(𝑥)𝑦 + 𝑄(𝑥)𝑦’ and there exist a function 𝜑(𝑥,𝑦) such that (𝛿𝜑/𝛿𝑥) = 𝑃(𝑥) and (𝛿𝜑/𝛿𝑦) = 𝑄(𝑥)

1^st-Order Linear DE

𝑓(𝑥) = 𝑃(𝑥)𝑦 + 𝑄(𝑥)𝑦’

• 1^st-Order Linear Homogenous DE: 0 = 𝑃(𝑥)𝑦 + 𝑄(𝑥)𝑦’
• 1st-Order Linear Constant Coefficient DE: 𝑓(𝑥) = 𝑝𝑦 + 𝑞𝑦’
• 1^st-Order Linear Constant Coefficient Homogenous DE: 0 = 𝑝𝑦 + 𝑞𝑦‘

Method of Separating Variables

solves first-order separable differential equations

Method of Integrating Factor

solves first-order non-separable linear differential equations

Method for Homogenous DE

solves first-order homogenous non-separable non-linear differential equations

Solving Exact DE

solves first-order exact differential equations