Exercises for Question Type 2: Sketching a solution curve that passes through a specific point using a slope field diagram

Question 1

On a coordinate plane, construct the slope field for \frac{d y}{d x} = y - x . Sketch the solution curve that passes through the point (1, 0) .

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Question 2

Construct the slope field for \frac{d y}{d x} = sin (x) + y and sketch the solution curve that goes through (π, 0) .

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Question 3

The question requires drawing a slope field for a given first-order differential equation and sketching a specific solution curve passing through a given point.

Draw the slope field for \frac{d y}{d x} = - \frac{x}{y} on the grid provided below and sketch the solution curve passing through the point (1, 1) . Draw on this

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Question 4

The following grid shows the points where the slope field for the differential equation \frac{d y}{d x} = \frac{y - 2}{x + 1} (for x \neq = - 1) is to be constructed.

On the grid provided in the specification, construct the slope field for the differential equation \frac{d y}{d x} = \frac{y - 2}{x + 1} at the 20 indicated points where x \in {- 3, - 2, 0, 1} and y \in {0, 1, 2, 3, 4} . Hence, sketch the particular solution to the differential equation that passes through the point (0, 3) .

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Question 5

Sketch the slope field for \frac{d y}{d x} = e^{- x} - y and draw the solution curve that passes through the point (0, 1) .

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Question 6

Differential Equations

On graph paper, sketch the slope field for the logistic differential equation \frac{d y}{d x} = y (1 - y) and draw the particular solution through (0, 0.5) .

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Question 7

On the coordinate grid below, draw the slope field for the differential equation \frac{d y}{d x} = x + y for x, y \in [- 3, 3] . Then sketch the particular solution curve passing through the point (0, 1) . Draw on this

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Question 8

On graph paper, draw the slope field for the differential equation \frac{d y}{d x} = \frac{y}{x} for x \neq = 0 and sketch the particular solution passing through the point (1, 2) .

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Question 9

This question assesses the ability to draw a slope field for a first-order differential equation and to sketch a particular solution curve passing through a given point.

On the coordinate grid provided below: (a) Draw the slope field for the differential equation \frac{d y}{d x} = x y . (b) Sketch the particular solution curve that passes through the point (1, 2) . Draw on this

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Question 10

Level: HL Paper: 1

On a set of axes, construct the slope field for the differential equation \frac{d y}{d x} = x^{2} - y for the domain - 2 \leq x \leq 2 and range - 1 \leq y \leq 3, evaluating the slopes at all integer grid points. Sketch the particular solution that passes through the point (- 1, 2) .

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Question 11

Draw the slope field for the differential equation \frac{d y}{d x} = y^{2} - x^{2} for x, y \in {- 1, 0, 1, 2}, and sketch the particular solution curve passing through the point (1, 1) .

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IB Mathematics Applications & Interpretation Question Type 2: Sketching a Solution Curve That Passes Through a Specific Point Using a Slope Field Diagram Exercises