Question

3. Use the MATLAB ode45 function to solve the following initial value problems. (a) Scalar equation x' = x + sin(t), x(0) = 1. Generate the plot of the solution for t ? [0, 2]. (b) System x' = x - 4y, y' = 4x - 7y, with initial condition x(0) = 0, y(0) = -1. Plot y against x for t ? [0, 2]. (c) Nonlinear oscillator x'' + 8.9x' + 0.1 sin x = 0, x(0) = 0, x'(0) = -1. Generate the plot for x(t) for t ? [0, 10].

          3. Use the MATLAB ode45 function to solve the following initial value problems.

(a) Scalar equation
x' = x + sin(t), x(0) = 1.
Generate the plot of the solution for t ? [0, 2].

(b) System
x' = x - 4y,
y' = 4x - 7y,
with initial condition x(0) = 0, y(0) = -1. Plot y against x for t ? [0, 2].

(c) Nonlinear oscillator
x'' + 8.9x' + 0.1 sin x = 0, x(0) = 0, x'(0) = -1.
Generate the plot for x(t) for t ? [0, 10].

3. Use the MATLAB ode45 function to solve the following initial value problems.

(a) Scalar equation
x' = x + sin(t), x(0) = 1.
Generate the plot of the solution for t ? [0, 2].

(b) System
x' = x - 4y,
y' = 4x - 7y,
with initial condition x(0) = 0, y(0) = -1. Plot y against x for t ? [0, 2].

(c) Nonlinear oscillator
x” + 8.9x' + 0.1 sin x = 0, x(0) = 0, x'(0) = -1.
Generate the plot for x(t) for t ? [0, 10].

Added by Allen S.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Ryan Conley

08/19/2020

Step 1

Scalar equation: First, we need to define the function for the differential equation and the initial condition. Then, we use ode45 to solve the equation and plot the solution. ```MATLAB % Define the function f = @(t, y) -sin(t); % Initial condition y0 = 1; % Show more…

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Use the MATLAB ode45 function to solve the following initial value problems: Scalar equation: x' = x + sin(t), x(0) = 1. Generate the plot of the solution for t ∈ [0, 2]. System: x' = x - 4y, y' = 4x - 7y, with initial condition x(0) = 0, y(0) = -1. Plot y against x for t ∈ [0, 2]. Nonlinear oscillator: x'' + 8.9x' + 0.1 sin x = 0, x(0) = 0, x'(0) = -1. Generate the plot for x(t) for t ∈ [0, 10].