Math Problem Statement
Choose the correct answer. (1) A first order differential equation of the form y′ = f(x) is called ········· variable. (A) Non-separable (B) Linear (2) If f(x)dy = g(y)dx, then (C) Exact (D) Separable
Solution
Let's break down both parts of the question:
(1) "A first-order differential equation of the form is called..."
- This equation has the form , which does not involve the variable on the right-hand side. This is a simple form of a linear differential equation. In this case, it's called Linear because it's of the form , where the derivative of is a function of only and doesn't involve nonlinear terms.
Thus, the correct answer for (1) is: (B) Linear
(2) "If , then the differential equation is..."
- This equation can be rewritten as: which is a separable differential equation because the variables and can be separated on opposite sides of
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Differential Equations
First-Order Equations
Linear Equations
Separable Equations
Formulas
y' = f(x)
f(x)dy = g(y)dx
\frac{dy}{g(y)} = \frac{dx}{f(x)}
Theorems
Separable Differential Equations
Linear Differential Equations
Suitable Grade Level
Undergraduate Mathematics
Related Recommendation
Solving First Order Differential Equations Using Separation of Variables
Solve First-Order Differential Equations Using Integrating Factor and Separation
Differential Equations: Identifying and Solving First-Order Equations
Solution of Scalar First-Order Differential Equations: Separable, Linear, and Exact Forms
Solving First-Order Differential Equations with Various Methods