Can the Euler approximation method be used to solve higher order DE?(adsbygoogle = window.adsbygoogle || []).push({});

I have ##\ddot x=\omega^2 x## which i rewrite as ##y''=\omega^2y##. initial conditions y(0)=0, y'(0)=1.

The Euler method: ##y_{n+1}=y_n+h\cdot y'_n##. i use this to make:

$$y''_{n+1}=y'_n+h\cdot y''_n~~\rightarrow~~\omega^2y_{n+1}=y'_n+h\omega^2 y_n$$

$$\omega^2(y_n+hy'_n)=y'_n+h\omega^2 y_n$$

$$\rightarrow~y'_n=\left[ \frac{\omega^2(1-h)}{1-\omega^2h} \right]y_n$$

But this contradicts the initial condition y'(0)=1, after i substitute y(0)=0 in the formula i found.

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# B Euler's method for second order DE

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