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Question Number 93451 by mhmd last updated on 13/May/20

$$Solvebyusingchangetheconistantmegbod$$$$4y^{{}^{″}}+y=\frac{x^2-1}{x\sqrt{x}}?$$

Commented by i jagooll last updated on 13/May/20

$$\mathrm{what}\mathrm{is}\mathrm{conistant}\mathrm{megbod}?$$

Commented by mhmd last updated on 13/May/20

$$sorymethodnotmegbod$$

Commented by john santu last updated on 13/May/20

$$\mathrm{characteristic}\mathrm{eq}:{4\mathrm{r}}^2+1=0$$$$\mathrm{r}=\pm \frac{1}{2}i.\mathrm{homogenous}\mathrm{solution}$$$${\mathrm{y}}_{\mathrm{h}}={\mathrm{C}}_1{\mathrm{e}}^{\frac{1}{2}i}+{\mathrm{C}}_2{\mathrm{e}}^{-\frac{1}{2}i}$$$${\mathrm{y}}_{\mathrm{h}}={\mathrm{C}}_1\cos \left(\frac{1}{2}x\right)+{\mathrm{C}}_2\sin \left(\frac{1}{2}x\right)$$$$\mathrm{Particular}\mathrm{solution}$$$${\mathrm{y}}_{\mathrm{p}}=\frac{\sqrt{x}-x^{-3/2}}{{4\mathrm{D}}^2+1}$$

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