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Question Number 142079 by rs4089 last updated on 26/May/21

$$y=\frac{dy}{dx}+\frac{d^{2}y}{{dx}^2}+\frac{d^{3}y}{{dx}^3}+.....$$$$solvethisdiffrentialequation$$

Answered by Dwaipayan Shikari last updated on 26/May/21

$$y=y^{\prime }+y^{″}+y^{{}^{‴}}+...y={Ce}^{\lambda x}$$$$e^{\lambda x}=\lambda e^{\lambda x}+{\lambda }^2{e}^{\lambda x}+...$$$$1=\lambda +{\lambda }^2+{\lambda }^3+...\Rightarrow 1=\frac{\lambda }{1-\lambda }\Rightarrow \lambda =\frac{1}{2}$$$$y=C\sqrt{e^x}$$

Answered by mindispower last updated on 26/May/21

$$y=y^{\prime }+y^{\prime }\Rightarrow y=2y^{\prime }\Rightarrow y={ke}^{\frac{x}{2}}$$

Answered by mnjuly1970 last updated on 26/May/21

$$y^{\prime }=-y^{\prime }+y$$$$y^{\prime }=\frac{y}{2}....\gg ln\left(y\right)=\frac{x}{2}+C$$$$......y={ke}^{\frac{x}{2}}.....$$

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