differential equation Lecture #2
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This document summarizes lecture 2 on differential equations of first order and first degree. It discusses the definition of a differential equation of first order and first degree as one of the form dy/dx = f(x,y). It then describes two types of these differential equations - variable separable form, where the equation can be written as f(x,y)=M(x)N(y) or f(x,y)=M(x)/N(y), and provides an example of solving this type by integrating both sides.
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differential equation Lecture #2
- 1. DIFFERENTIAL EQUATION (MT-201) SYED AZEEM INAM DIFFERENTIAL EQUATION (MT-201) LECTURE #2 DIFFERENTIAL EQUATIONS OF FIRST ORDER AND FIRST DEGREE: The differential equations of the type dy=f(x,y) is known as a differential equation of first order and first degree. We shall now discuss various types of differential equations of first order and first degree by providing some examples. TYPE I: VARIABLE SEPARABLE FORM A differential equation of the form 𝑑𝑦 𝑑𝑥 = 𝑓(𝑥, 𝑦) → (1) is separable if we may write f(x,y)=M(x).N(y) or f(x,y)=M(x)/N(y),where M(x) and N(y) are real values functions of x and y respectively. Thus equation (1) is equivalent to N(y)dy=M(x)dx. The solution of this equation is obtained on integrating it.