How do you use ode45( ) when the equation is not in dy/dt form?

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ssmith 2021-11-19

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评论： Star Strider 2021-11-23

I have an equation that I need to approximate the solution for using ode45( ) with initial values y(0) = 1 and y'(0) = 0 on interval of 0 < t < 150 and then plot x(t)

So far I have this for the equation y" + 4y = sin(1.9t)

syms y(t) 
eqn = diff(y,2) + 4*y == sin(1.9*t)
V = odeToVectorField(eqn) 

I know if the equation was in the form of dy/dt = sin(1.9t) - 4y then it would be

k = @(t,y) sin(1.9*t)-4*y;
[t,y] = oder45(k,[0,150])
plot(t,y)

But I do not know know how to write it for the form that my equation is in at this moment

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回答（2 个）

Paul 2021-11-19

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https://ww2.mathworks.cn/matlabcentral/answers/1591094-how-do-you-use-ode45-when-the-equation-is-not-in-dy-dt-form#answer_835959

Check out this link ....

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ssmith 2021-11-19

@Paul Do you have an example that shows how to apply initial conditions?

Paul 2021-11-19

在 MATLAB Online 中打开

It's shown on the the doc page at that link. Or check

doc ode45

to see how to specifcy the initial conditions

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Star Strider 2021-11-19

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1591094-how-do-you-use-ode45-when-the-equation-is-not-in-dy-dt-form#answer_835969

在 MATLAB Online 中打开

Since the equation as written involves the second derivative, it is also necessary to define the first derivative as a separate element of the resulting system of first-order differential equatiions.

The odeToVectorField function does this (I added the second ‘substitutions’ output to illustrate what the function actually does) —

syms y(t)

eqn = diff(y,2) + 4*y == sin(1.9*t)

eqn(t) =