Please solve the following (read instucions carefully) The exercise presents six slope fields labeled A through F and six differential equations labeled 1 through 6. The task is to match four of the slope fields with their corresponding differential equations.**Slope Fields:**- **Graph A:** Displays concentric circles with arrows indicating a rotational flow centered at the origin.- **Graph B:** Features vertical lines, indicating solutions that move toward and away from the y-axis, creating a pattern that seems to diverge from the origin.**Differential Equations:**1. \( y'(x) = x + y \)2. \( y'(x) = x + y + 1 \)3. \( y'(x) = x + y - 1 \)4. \( y'(x) = -\frac{y}{x} \)5. \( y'(x) = -\frac{x}{y} \)6. \( y'(x) = x^2 + y^2 \)Each slope field represents a visual depiction of the solution trajectories that satisfy one of the differential equations. The aim is to correctly pair each graph with its equation using the characteristics of the field and theoretical knowledge of differential equations.Visitors to the educational website can select the equations corresponding to each slope field from dropdown menus linked to graphs A through F for an interactive matching experience. The image contains a series of vector field plots labeled C, D, E, and F. Each plot is separated by a horizontal red line.### C. Vector Field- **Description**: The field lines are mostly horizontal, with gradual curvature near the center. This suggests a constant field with a slight perturbation.- **Axes**: The x and y axes range from -4 to 4.### D. Vector Field- **Description**: This field shows a symmetrical pattern about the y-axis, with vectors diverging outward from the center.- **Axes**: Similar to C, with x and y ranging from -4 to 4.### E. Vector Field- **Description**: The vectors curve downward to the right, indicating a rotational dynamic with a downward flow.- **Axes**: The grid shows values from -4 to 4 on both axes.### F. Vector Field- **Description**: The vectors curve upward as they progress to the right, highlighting an upward circular flow.- **Axes**: Maintains the same range as others from -4 to 4.These vector fields visually represent different flow dynamics and can be used to study vector calculus, fluid dynamics, or electromagnetic fields.

There are six slope fields labeled A through F. There are six differential equations labeled 1 through 6. Four of the given slope fields have their corresponding differential equation within the given list. Find, and match up, these corresponding pairs.

There are six slope fields labeled A through F. There are six differential equations labeled 1 through 6. Four of the given slope fields have their corresponding differential equation within the given list. Find, and match up, these corresponding pairs.

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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