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Question Number 183211 by Mastermind last updated on 23/Dec/22

$${\mathrm{y}}^{\left(\mathrm{iv}\right)}+{16\mathrm{y}}^{\left(\mathrm{iii}\right)}+{9\mathrm{y}}^{\left(\mathrm{ii}\right)}+{256\mathrm{y}}^{\left(\mathrm{i}\right)}+256\mathrm{y}=0$$$$$$$$$$$$\mathrm{M}.\mathrm{m}$$

Answered by aleks041103 last updated on 23/Dec/22

$$y=e^{rx}$$$$\Rightarrow r^4+16r^3+9r^2+256r+256=0$$$$r=r_{1,2,3,4}$$$$\Rightarrow y\left(x\right)={Ae}^{r_{1}x}+{Be}^{r_{2}x}+{Ce}^{r_{3}x}+{De}^{r_{4}x}$$

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