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Eswin Paul T
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I have a first order bernoullis differential equation. I need to solve this in matlab. Can anyone help me?
What is the context of the question? Is this for schoolwork?Eswin Paul T said:I have a first order bernoullis differential equation. I need to solve this in matlab. Can anyone help me?
I am working on lidars to retrieve extinction coefficient. I have to solve the lidar equation using Klett method which involves reducing the lidar eqn to a first order bernoullis equation.berkeman said:What is the context of the question? Is this for schoolwork?
What is your level of experience with MATLAB? What is the DE (and the initial conditions), and which numerical method do you have in mind for solving it?
y0 = 0.1;
tspan = [0.5 20];
[x,y] = ode45(@bernoulli1, tspan, y0);
plot(x,y)
function dydx = bernoulli1(x,y)
% This function codes the equations and
% is called at each time step by ode45 to
% advance the integration.
dydx = x*y^2 - y*(1/x);
end
Bernoulli's differential equation is a type of first-order nonlinear ordinary differential equation, named after Swiss mathematician Daniel Bernoulli. It has the form dy/dx + P(x)y = Q(x)y^n, where P(x) and Q(x) are functions of x and n is a constant. It is commonly used in physics and engineering to model various physical phenomena.
There are several ways to solve Bernoulli's differential equation in MATLAB. One way is to use the built-in function dsolve
, which can symbolically solve differential equations. Another way is to use numerical methods, such as ode45
or ode23
, which can numerically approximate the solution.
The syntax for solving Bernoulli's differential equation using dsolve
is dsolve('dy/dx + P(x)y = Q(x)y^n', 'y(x)')
, where P(x)
and Q(x)
are the functions in the equation and y(x)
is the dependent variable. For numerical methods, the syntax varies depending on the specific method being used.
Yes, you can graph the solution to Bernoulli's differential equation in MATLAB using the ezplot
function. The syntax is ezplot('y(x)', [a, b])
, where y(x)
is the solution and [a, b]
is the interval over which to plot the graph.
Yes, when using numerical methods, it is important to choose appropriate initial conditions and to ensure that the solution does not contain any singularities. Additionally, the value of n in the equation must be carefully selected to avoid division by zero. It is also important to check the accuracy and stability of the solution obtained.