Math, asked by adhikarysayan, 11 months ago

X*dy/dx
= y(logy - logx + 1)

Answers

Answered by anubhavsgautam
0

Answer:

x\frac{dy}{dx} = y(logy -logx +1)\\\\\frac{dy}{dx} = \frac{y}{x}(logy - logx +1)\\ \\\frac{y}{x} = V\\\\logy-logx = V \\\\  dy/dx= V+x \frac{dv}{dx}\\\\

V+ x\frac{dv}{dx} = V ( logV + 1 )\\\\\\x\frac{dv}{dx}=VlogV\\\\\int\ {\frac{1}{VlogV}} \, dv =\int\ {x} \, dx \\\\log(logV)= x^{2} /2 +c\\\\log(log \frac{y}{x})= x^{2} /2 +c\\\\log \frac{y}{x}= e^{x^{2}/2 + c }

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