Answer to Question #203270 in MatLAB for sumu

Question #203270

How to express a 3rd order differential equation into three first order differential equations?

Explain.


1
Expert's answer
2021-06-06T12:59:24-0400

Let's 3rd order differential equation is y(t)=f(t,y,y,y)y'''(t) = f(t, y, y', y''). let introduce new vector-function x(t)\overrightarrow{x}(t)

x=[x1(t)x2(t)x3(t)]=[y(t)y(t)y(t)]\overrightarrow{x} = \begin{bmatrix} x_1(t) \\ x_2(t) \\ x_3(t) \end{bmatrix} = \begin{bmatrix} y(t) \\ y'(t) \\ y''(t) \end{bmatrix}

then

dxdt=ddt[y(t)y(t)y(t)]=[x2(t)x3(t)f(t,x1(t),x2(t),x3(t)]\frac{d \overrightarrow{x}}{d t} = \frac{d }{d t} \begin{bmatrix} y(t) \\ y'(t) \\ y''(t) \end{bmatrix} = \begin{bmatrix} x_2(t) \\ x_3(t) \\ f(t, x_1(t), x_2(t), x_3(t) \end{bmatrix}


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