Question

The solution of the differential equation $(y+x^{2})dx=xdy, x>0$ is a curve which passes through the point (1,0). The equation of the curve is

• A. $y=x(x+1)$
• B. $y=x(x-1)$
• C. $y=x^{2}(x-1)$
• D. $y=x^{2}(x+1)$
• E. $y=x(x^{2}-1)$

Hint:

Logic Tip: Alternatively, rewrite as $\frac{dy}{dx} - \frac{1}{x}y = x$. This is a standard linear differential equation of the form $\frac{dy}{dx} + Py = Q$. The Integrating Factor is $e^{\int -\frac{1}{x} dx} = e^{-\ln x} = \frac{1}{x}$. Multiplying through yields $d(\frac{y}{x}) = dx$.

Answer 1

The Correct Option is B