Question

Let $y = y(x)$ be the solution curve of the differential equation, $\left(y^{2}-x\right) \frac{dy}{dx}=1,$ satisfying $y(0) = 1$. This curve intersects the x-axis at a point whose abscissa is :

• A. $2 + e$
• B. $2$
• C. $2 - e$
• D. $-e$

Answer 1

Answer: (C)

$\left(y^{2}-x\right) \frac{dy}{dx}=1$
$\Rightarrow \frac{dx}{dy}+x=y^{2}$
$I.F.=e^{\int dy}=e^{y}$
Solution is given by
$x\,e^{y}=\left(y^{2}-2y+2\right)e^{y}+C$
$x = 0, y = 1$, gives $C = -e$
If $y = 0$, then $x = 2 - e$