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Question Number 34051 by adil last updated on 29/Apr/18

$$2dy/dx+y=0y\left(0\right)=-3$$

Answered by candre last updated on 30/Apr/18

$$2\frac{dy}{dx}+y=0$$$$\frac{dy}{dx}=-\frac{y}{2}$$$$\frac{dy}{y}=-\frac{dx}{2}$$$$\int \frac{dy}{y}=-\int \frac{dx}{2}$$$$\ln y=-\frac{x}{2}+K$$$$y={ce}^{-x/2}$$$$x=0\Rightarrow c=-3\Rightarrow y=-3e^{-x/2}$$

Commented by candre last updated on 30/Apr/18

$$\underset{-3}{\stackrel{y}{\int }}\frac{dy}{y}=-\frac{1}{2}\underset{0}{\stackrel{x}{\int }}dx$$$$\ln y-\ln (-3)=\ln \frac{y}{-3}=-\frac{x}{2}$$$$y=-3e^{-\frac{x}{2}}$$

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