A-LevelMathematicsDifferential equations9709/32 · Oct/Nov 2018 · Q68 Marks
A certain curve is such that its gradient at a general point with coordinates (x, y) is proportional to y²/x The curve passes through the points with coordinates (1, 1) and (e, 2). By setting up and solving a differential equation, find the equation of the curve, expressing y in terms of x.
- A certain curve is such that its gradient at a general point with coordinates (x, y) is proportional to y2 X The curve passes through the points with coordinates (1, 1) and (e, 2). By setting up and solving a differential equation, find the equation of the curve, expressing y in terms of x.[8]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2018). The mark or mark type is shown in brackets.
- [B1] State equation dy/dx = k y²/x or equivalent
- [B1] Separate variables correctly and integrate at least one side
- [B1+B1] Obtain terms -1/y and k lnx
- [M1] Use given coordinates correctly to find k and/or a constant of integration C in an equation containing terms -1/y, blnx and C
- [A1+A1] Obtain k = 1/2 and c = – 1, or equivalent
- [A1] Obtain answer y = 2/(2-lnx), or equivalent, and ISW
Write your answer and get it marked
On Oracle Prep you can write or photograph your own answer and have it marked by AI against this mark scheme, with feedback on what you missed.
Sign up free →