Solve ydx - xdy + log x dx
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The given differential equation is ydx – xdy + lnxdx = 0 y - x(dy/dx) + lnx = 0
x(dy/dx) - y = lnx dy/dx - (y/x) = lnx/x ...(i) which is a linear differential equation IF = e-∫dx/x = e-log x = 1/x Multiplying both sides of Eq. (i) by IF and integrating, we get y.(IF) = ∫Q.(IF) dx + c y.(1/x) = ∫(lnx/x2) dx + c y/x = - ((log x/x) + (1/x)) + c y = – (log x + 1) + cRead more on Sarthaks.com - https://www.sarthaks.com/561597/solve-ydx-xdy-lnxdx-0
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