Let a particle move in the plane with and

MATHEMATICS · Multi-part · AP · Calculus BC · Parametric, Polar, and Vector-Valued Functions · Parametric, Polar, and Vector-Valued Functions

Problem

Let a particle move in the plane with

\dfrac{dx}{dt}=e^{2t}

and

\dfrac{dy}{dx}=x^{2}+1

. At time

t=0

the particle is at the point

(1,2)

. (a) Determine

x(t)

for all

t\ge 0

. (b) Using your result from part (a), obtain

y(t)

for all

t\ge 0

. Show all algebraic steps. (c) Find the exact coordinates of the particle when

t=\ln 2

. State your answer as an ordered pair.