### Math NomenclatureTouch base for some math nomenclatures. Optimize to 1 to 1 and use all if there are 1 to more connections.#### Options:1. **An equation for electric current**2. **An equation for a linear curve**3. **A constant**4. **A 1st order differential equation**5. **A 2nd order differential equation**6. **An ordinary differential equation (1st order)**7. **A partial differential equation**8. **An integration equation**#### Choices:A. $ I = \frac{V}{R} $B. $ y' = 8x + 6 $C. \[ y = \int_{0}^{100}{(8x + 6)dx} \]D. $ y' - 8x - 6 = 0 $E. $ y'' = 8 $F. $ y = 8x + 6 $G. $ dz = 8x\,dx + 8y $H. 12.23154687854### Detailed Explanation of Equations:- **Equation for Electric Current:** - **Choice A:** $ I = \frac{V}{R} $ - This is Ohm's Law, representing the relationship between current (I), voltage (V), and resistance (R).- **Equation for a Linear Curve:** - **Choice F:** $ y = 8x + 6 $ - This is the equation of a straight line in slope-intercept form, where 8 is the slope and 6 is the y-intercept.- **A Constant:** - **Choice H:** 12.23154687854 - This is a constant value.- **1st Order Differential Equation:** - **Choice B:** $ y' = 8x + 6 $ - This represents a first-order differential equation, where $ y' $ denotes the first derivative of y with respect to x.- **2nd Order Differential Equation:** - **Choice E:** $ y'' = 8 $ - This is a second-order differential equation, where $ y'' $ denotes the second derivative of y with respect to x.- **Ordinary Differential Equation (1st Order):** - **Choice D:** \(

Answered: Image /qna-images/answer/3c7ac50e-4459-4220-9b85-d8d74a73b05d.jpg

An equation for electric current A. I = V/R В. у' %3 8х + 6 An equation for a linear curve 100 С. y= I (8x + 6)dx a constant A 1st order differential equation D.y'-8x-6 = 0 A 2nd order differential equation Е. у" %3D 8 An ordinary differential equation (1st order) F. Y = 8x +6 G. dz = 8xdx + 8dy A partial differential equation H. 12.23154687854 An integration equation

An equation for electric current A. I = V/R В. у' %3 8х + 6 An equation for a linear curve 100 С. y= I (8x + 6)dx a constant A 1st order differential equation D.y'-8x-6 = 0 A 2nd order differential equation Е. у" %3D 8 An ordinary differential equation (1st order) F. Y = 8x +6 G. dz = 8xdx + 8dy A partial differential equation H. 12.23154687854 An integration equation

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

### Math Nomenclature

Touch base for some math nomenclatures. Optimize to 1 to 1 and use all if there are 1 to more connections.

#### Options:

1. **An equation for electric current**
2. **An equation for a linear curve**
3. **A constant**
4. **A 1st order differential equation**
5. **A 2nd order differential equation**
6. **An ordinary differential equation (1st order)**
7. **A partial differential equation**
8. **An integration equation**

#### Choices:

A. $ I = \frac{V}{R} $

B. $ y' = 8x + 6 $

C. \[ y = \int_{0}^{100}{(8x + 6)dx} \]

D. $ y' - 8x - 6 = 0 $

E. $ y'' = 8 $

F. $ y = 8x + 6 $

G. $ dz = 8x\,dx + 8y $

H. 12.23154687854

### Detailed Explanation of Equations:

- **Equation for Electric Current:**
- **Choice A:** $ I = \frac{V}{R} $
- This is Ohm's Law, representing the relationship between current (I), voltage (V), and resistance (R).

- **Equation for a Linear Curve:**
- **Choice F:** $ y = 8x + 6 $
- This is the equation of a straight line in slope-intercept form, where 8 is the slope and 6 is the y-intercept.

- **A Constant:**
- **Choice H:** 12.23154687854
- This is a constant value.

- **1st Order Differential Equation:**
- **Choice B:** $ y' = 8x + 6 $
- This represents a first-order differential equation, where $ y' $ denotes the first derivative of y with respect to x.

- **2nd Order Differential Equation:**
- **Choice E:** $ y'' = 8 $
- This is a second-order differential equation, where $ y'' $ denotes the second derivative of y with respect to x.

- **Ordinary Differential Equation (1st Order):**
- **Choice D:** \(

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