Exercises for Question Type 1: Finding the general solution to linear coupled differential equations with real and distinct eigenvalues

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Exercises for Question Type 1: Finding the general solution to linear coupled differential equations with real and distinct eigenvalues - IB

Question 1

Find the particular solution to the system of differential equations \frac{d x}{d t} = 4 x + y, \frac{d y}{d t} = 2 x + 3 y given that x (0) = 0 and y (0) = 3 .

[9]

Question 2

Find the general solution to the system \frac{d x}{d t} = 7 x + 3 y, \frac{d y}{d t} = 4 x + 2 y

[6]

Question 3

Find the general solution to the system \frac{d x}{d t} = 6 x + 2 y, \frac{d y}{d t} = 3 x + 5 y

[6]

Question 4

Find the general solution to the system of differential equations: \frac{d x}{d t} = 4 x + y \frac{d y}{d t} = 2 x + 3 y

[7]

Question 5

Find the particular solution to the system ⎩ ⎨ ⎧ \frac{d x}{d t} = 2 x + y \frac{d y}{d t} = 3 y given x (0) = 4 and y (0) = 2 .

[4]

Question 6

The system of differential equations is given by: {\frac{d x}{d t} = 2 x + y \frac{d y}{d t} = 3 y

Find the general solution to the system of differential equations: \frac{d x}{d t} = 2 x + y, \frac{d y}{d t} = 3 y

[6]

Question 7

Find the particular solution to the system \frac{d x}{d t} = x + 2 y, \frac{d y}{d t} = 4 y given x (0) = 3 and y (0) = 1 .

[6]

Question 8

Find the particular solution to the system \frac{d x}{d t} = 6 x + 2 y, \frac{d y}{d t} = 3 x + 5 y given x (0) = - 1 and y (0) = 2 .

[8]

Question 9

Find the particular solution to the system of differential equations \frac{d x}{d t} \frac{d y}{d t} = 5 x + 2 y = 2 x + 2 y given that x (0) = 1 and y (0) = 0 .

[7]

Question 10

Find the general solution to the system ⎩ ⎨ ⎧ \frac{d x}{d t} = 5 x + 2 y \frac{d y}{d t} = 2 x + 2 y

[6]

Question 11

Find the particular solution to the system \frac{d x}{d t} = 2 x + 3 y, \frac{d y}{d t} = - y given x (0) = 2 and y (0) = 1 .

[7]

Question 12

Find the general solution to the system of differential equations ⎩ ⎨ ⎧ \frac{d x}{d t} = x + 2 y \frac{d y}{d t} = 4 y

[6]

IB Mathematics Applications & Interpretation Question Type 1: Finding the General Solution to Linear Coupled Differential Equations with Real and Distinct Eigenvalues Exercises