A) \[y\frac{dy}{dx}-x{{\left( \frac{dy}{dx} \right)}^{2}}=1\]
B) \[\frac{x{{d}^{2}}y}{d{{x}^{2}}}+{{\left( \frac{dy}{dx} \right)}^{2}}=0\]
C) \[y\frac{dx}{dy}+x=1\]
D) None of these
Correct Answer: A
Solution :
[a] The equation of the tangent at the point \[R(x,f(x))\]is \[Y-f(x)=f'(x)(X-x)\] The coordinates of the point P are\[(0,f(x)-xf'(x))\]. The slope of the perpendicular line through P is \[\frac{f(x)-xf'(x)}{-1}=-\frac{1}{f'(x)}\] Or \[f(x)f'(x)-x{{(f'(x))}^{2}}=1\] Or \[\frac{ydy}{dx}-x{{\left( \frac{dy}{dx} \right)}^{2}}=1\] Which is the required differential equation to the curve at \[y=f(x).\]You need to login to perform this action.
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