New to matlab and not sure how to reduce to first order

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Samantha 2020-12-18

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编辑： James Tursa 2020-12-18

Solve the third-order ODE function

y′′′− 2 * y′′−(y′)^2 = 1

With tspan [0 5], y(0) = y’(0) = 0, y’’ = 1.

You need to reduce the given third-order ODE equation to standard 1st-order ODE equations before solving

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KSSV 2020-12-18

So integrate first w.r.t first, it will be reduced into y'' and then use ode45.

Jon 2020-12-18

Would this work? ode45 only solves first order equations, wouldn't you still have a second order equation

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Jon 2020-12-18

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编辑：Jon 2020-12-18

在 MATLAB Online 中打开

Define

y1 = y

y2 = y'

y3 = y''

% and then make a function f, for example put the code below into an m-file called f.m

function dydt = f(t,y)
dydt(1) = y(2); % y1' = y2
dydt(2) = y(3); % y'' = y3
dydt(3) = 1 + 2*y(3) + y(2)^2;

then use one of the ode solvers e.g ode45 passing it the function f described above

Please see https://www.mathworks.com/help/matlab/math/choose-an-ode-solver.html especially the section on solving higher order equation

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Jon 2020-12-18

You can get documentation for ode45 by typing doc ode45 on the command line.

Once you get this running, if you have not already done so I would highly recommend taking the time to complete the MATLAB on ramp training to help you get more familiar with using MATLAB in general https://www.mathworks.com/learn/tutorials/matlab-onramp.html

James Tursa 2020-12-18

编辑：James Tursa 2020-12-18

在 MATLAB Online 中打开

The ode45( ) call should not be inside your derivative function. That's backwards. The ode45( ) function is calling your derivative function, not the other way around. So you should have some code that defines initial conditions and calls ode45( ) like this:

tspan = [0 5]; % time span
y0 = [0 0 1]; % initial values of y, y', and y''
ode45(@odef,tspan,y0);
plot(t,y);

and then a separate code (e.g., in a file called odef.m, or maybe below the code listed above) that contains your derivative code:

function dydt = odef(t,y)
dydt = zeros(3,1); % the values y', y'', and y'''
dydt(1) = y(2); % y' = y2
dydt(2) = y(3); % y'' = y3
dydt(3) = 1 + 2*y(3) + y(2)^2; % y''' = 1 + 2y'' + (y')^2
end