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Let $f(x)$ be a given differentiable function. Consider the following differential equation in $y$ $$f(x) \frac{dy}{dx} = yf’(x)-y^2.$$ The general solution of this equation is given by

  1. $y=-\frac{x+c}{f(x)}$
  2. $y^2=\frac{f(x)}{x+c}$
  3. $y=\frac{f(x)}{x+c}$
  4. $y=\frac{\left[f(x)\right]^2}{x+c}$
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C)

Follow the following steps,

  1. Divide throughout by $f(x)$ and $y^2$.
  2. Consider $z=\frac{1}{y}$, you will get standard differential equation in $z$.
  3. Remember $$\int \frac{f’(x)}{f(x)}=\ln|f(x)| +c$$ you can ingore mod.
  4. Solve for $z$ and then sustitute $z=\frac{1}{y}$

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