HardMathematicsHigh School (11–12)Functions and CalculusNumerical

A surveyor describes the edge of a field by a curve of the family y = ax + b/x for x > 0, where a…

Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

A surveyor describes the edge of a field by a curve of the family $y = ax + \dfrac{b}{x}$ for $x > 0$ , where $a$ and $b$ are constants that change from field to field. She wants one equation that fits every field. The family has two constants, so she differentiates twice. After she eliminates $a$ and $b$ , the equation has the form $x^2y'' + xy' - y = 0$ . One particular field has $y(1) = 5$ and $y'(1) = 1$ . Find $a$ and $b$ for that field. Then find $y(2)$ and $y''(2)$ .

Need a reminder? The key ideaShow

To form the equation of a family with $n$ constants, differentiate $n$ times and eliminate the constants. The result has order $n$ . Read its degree after clearing roots.

\displaystyle y = mx \ \Rightarrow\ x\,y' = y.

The worked solution

Have you tried it?

Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

← All Problems

← A drawing compass is placed with its needle at the point (a, 0) on the x-axis, and the pencil is…A radio dish is modelled by a family of parabolas with the axis along the x-axis and the vertex at… →

More onFunctions and Calculus

Discussion (0)

Loading…