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Question Number 119002 by benjo_mathlover last updated on 21/Oct/20

$$\frac{dy}{dx}=\frac{xy}{x^2+1}andy\left(\sqrt{15}\right)=2$$

Answered by bramlexs22 last updated on 21/Oct/20

$$\frac{dy}{y}=\frac{xdx}{x^2+1}\Rightarrow \int \frac{dy}{y}=\int \frac{xdx}{x^2+1}$$$$\ln \left(y\right)=\frac{1}{2}\ln (x^2+1)+C$$$$\ln \left(y\right)=\ln \left(\lambda \sqrt{x^2+1}\right)\Rightarrow y=\lambda \sqrt{x^2+1}$$$$\Rightarrow 2=\lambda \sqrt{16};\lambda =\frac{1}{2}$$$$thereforey=\frac{\sqrt{x^2+1}}{2}$$

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