The general solution of {x^2}frac{{dy}}{{dx}} | vedclass

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Question

(B) Given the differential equation: ${x^2}\frac{{dy}}{{dx}} = 2$Step $1$: Separate the variables.$\frac{{dy}}{{dx}} = \frac{2}{{{x^2}}}$$dy = 2{x^{-2

Vedclass · Accepted Answer

$y = c - \frac{2}{x}$

Vedclass · Answer

(B) Given the differential equation: ${x^2}\frac{{dy}}{{dx}} = 2$Step $1$: Separate the variables.$\frac{{dy}}{{dx}} = \frac{2}{{{x^2}}}$$dy = 2{x^{-2}}dx$Step $2$: Integrate both sides.$\int dy = \int 2{x^{-2}}dx$$y = 2 \left( \frac{{{x^{-2+1}}}}{{-2+1}} \right) + c$$y = 2 \left( \frac{{{x^{-1}}}}{{-1}} \right) + c$$y = -\frac{2}{x} + c$Thus,the general solution is $y = c - \frac{2}{x}$.

The general solution of ${x^2}\frac{{dy}}{{dx}} = 2$ is

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