Question

X*dy/dx
= y(logy - logx + 1)
​

Answer 1

Answer:

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

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