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Question 1

Skill question

Using Euler’s method with step length $h=0.1$ , approximate $x$ and $y$ at $t=0.2$ for the system:

\frac{dx}{dt} = -x + y, \quad \frac{dy}{dt} = x + 2y,

with initial values $t=0$ , $x=2$ , $y=1$ .

Question 2

Skill question

Using Euler’s method with step length $h=0.5$ , approximate $x$ and $y$ at $t=1.0$ for the system:

\frac{dx}{dt} = t x + y, \quad \frac{dy}{dt} = x + t y,

with initial values $t=0$ , $x=1$ , $y=2$ .

Question 3

Skill question

Using Euler’s method with step length $h=0.1$ , approximate $x$ and $y$ at $t=0.2$ for the system:

\frac{dx}{dt} = x y, \quad \frac{dy}{dt} = x - y,

with initial values $t=0$ , $x=1$ , $y=1$ .

Question 4

Skill question

Using Euler’s method with step length $h=0.1$ , approximate $x$ and $y$ at $t=0.3$ for the system:

\frac{dx}{dt} = x - y + t, \quad \frac{dy}{dt} = x + y^2,

with initial values $t=0$ , $x=1$ , $y=0$ .

Question 5

Skill question

Using Euler’s method with step length $h=0.1$ , approximate $x$ and $y$ at $t=0.2$ for the system:

\frac{dx}{dt} = x^2 - y, \quad \frac{dy}{dt} = y^2 - x + t,

with initial values $t=0$ , $x=0$ , $y=1$ .

Question 6

Skill question

Using Euler’s method with step length $h=0.2$ , approximate $x$ and $y$ at $t=0.6$ for the system:

\frac{dx}{dt} = t + x, \quad \frac{dy}{dt} = y - t,

with initial values $t=0$ , $x=0$ , $y=2$ .

Question 7

Skill question

Using Euler’s method with step length $h=0.5$ , approximate $x$ and $y$ at $t=2.0$ for the system:

\frac{dx}{dt} = x - y + 2t, \quad \frac{dy}{dt} = 3x + y^2,

with initial values $t=1$ , $x=2$ , $y=0$ .

Question 8

Skill question

Using Euler’s method with step length $h=0.1$ , approximate $x$ and $y$ at $t=0.4$ for the system:

\frac{dx}{dt} = x^2 + y^2, \quad \frac{dy}{dt} = 2x - y + t^2,

with initial values $t=0$ , $x=4$ , $y=2$ .

Question 9

Skill question

Using Euler’s method with step length $h=0.2$ , approximate $x$ and $y$ at $t=1.6$ for the system:

\frac{dx}{dt} = 2x + 3y, \quad \frac{dy}{dt} = x - y + t,

with initial values $t=1$ , $x=0$ , $y=1$ .

Question 10

Skill question

Using Euler’s method with step length $h=0.2$ , approximate $x$ and $y$ at $t=0.4$ for the system:

\frac{dx}{dt} = x + t^2 y, \quad \frac{dy}{dt} = t x^2 - y,

with initial values $t=0$ , $x=1$ , $y=1$ .

Question 11

Skill question

Using Euler’s method with step length $h=0.2$ , approximate $x$ and $y$ at $t=0.8$ for the system:

\frac{dx}{dt} = x^2 + y^2, \quad \frac{dy}{dt} = 2x - y + t^2,

with initial values $t=0$ , $x=4$ , $y=2$ .

Question 12

Skill question

Using Euler’s method with step length $h=0.5$ , approximate $x$ and $y$ at $t=2.0$ for the system:

\frac{dx}{dt} = x^2 + y^2, \quad \frac{dy}{dt} = 2x - y + t^2,

with initial values $t=0$ , $x=4$ , $y=2$ .

Question Type 3: Approximating values for coupled system using Euler's method for a given step length Exercises