Question

A curve y = f(x) has the property that the slope of tangent to the curve at every point is reciprocal to the y value of the curve. Write down a differential equation whose solution is y = f(x). No need to solve this equation.

Answer 1

If our function is y...


`slope of tangent to the curve at every point`
that would be this,\[\Large\bf\sf \frac{dy}{dx}\]
`is`\[\Large\bf\sf =\]
`the reciprocal to the y value of the curve`\[\Large\bf\sf \frac{1}{y}\]

Answer 2

\[\Large\bf\sf \frac{dy}{dx}\quad=\quad \frac{1}{y}\]Mmm I think that's all they were looking for, yes? :o

Answer 3

yea thats it thanks