The solution of the differential equation {x^ | vedclass

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Question

(C) Given differential equation is ${x^2}dy = - 2xydx$.Rearranging the terms to separate the variables,we get:$\frac{1}{y}dy = - \frac{2x}{x^2}dx$Simp

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${x^2}y = c$

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(C) Given differential equation is ${x^2}dy = - 2xydx$.Rearranging the terms to separate the variables,we get:$\frac{1}{y}dy = - \frac{2x}{x^2}dx$Simplifying the right side:$\frac{1}{y}dy = - \frac{2}{x}dx$Integrating both sides:$\int \frac{1}{y}dy = - 2 \int \frac{1}{x}dx$$\log |y| = - 2 \log |x| + C$Using the property of logarithms $n \log a = \log a^n$:$\log |y| = \log |x|^{-2} + \log c$$\log |y| = \log |c x^{-2}|$Taking the exponential of both sides:$y = c x^{-2}$Multiplying by $x^2$:${x^2}y = c$

The solution of the differential equation ${x^2}dy = - 2xydx$ is

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