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Question Number 115632 by m173 last updated on 27/Sep/20

Commented by m173 last updated on 27/Sep/20

find general solution

Commented by MJS_new last updated on 27/Sep/20

$$y=c\sin x\mathrm{is}\mathrm{already}\mathrm{the}\mathrm{solution}?!$$

Commented by mohammad17 last updated on 27/Sep/20

$$y=csin\left(x\right)\to \left(1\right)$$$$$$$$y^{{}^{\prime }}=ccos\left(x\right)\to \left(2\right)$$$$$$$$\frac{\left(2\right)}{\left(1\right)}\Rightarrow \frac{y^{{}^{\prime }}}{y}=cot\left(x\right)\Rightarrow y^{{}^{\prime }}=ycot\left(x\right)$$$$$$$$(m.o)$$

Commented by MJS_new last updated on 27/Sep/20

$$\mathrm{why}\mathrm{are}\mathrm{you}\mathrm{doing}\mathrm{what}\mathrm{are}\mathrm{you}\mathrm{doing}?$$

Commented by Dwaipayan Shikari last updated on 27/Sep/20

$$\mathrm{sinx}=\frac{\mathrm{y}}{\mathrm{c}}$$$$\mathrm{x}=\mathrm{k}\pi \pm {\sin }^{-1}\left(\frac{\mathrm{y}}{\mathrm{c}}\right)$$

Commented by mathmax by abdo last updated on 27/Sep/20

$$\mathrm{i}\mathrm{think}\mathrm{the}\mathrm{Q}\mathrm{here}\mathrm{find}\mathrm{the}\mathrm{diff}.\mathrm{equation}\mathrm{verified}\mathrm{by}\mathrm{y}..!$$$${\mathrm{y}}^{{}^{\prime }}=\mathrm{ccosx}\Rightarrow {\mathrm{y}}^{{}^{″}}=-\mathrm{csinx}=-\mathrm{y}\Rightarrow {\mathrm{y}}^{{}^{″}}+\mathrm{y}=0$$

Answered by PRITHWISH SEN 2 last updated on 27/Sep/20

$$\mathrm{I}\mathrm{think}$$$$\sin \mathrm{x}=\frac{\mathrm{y}}{\mathrm{c}}=\sin \alpha \left(\mathrm{say}\right)$$$$\mathrm{x}=\mathrm{n}\pi +{(-1)}^{\mathrm{n}}{\sin }^{-1}\left(\frac{\mathrm{y}}{\mathrm{c}}\right)\mathrm{n}\in \mathbb{N}$$

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