d^2y/dx^2 − dy/dx − 3/4 y = 0,
y(0) = 1, dy/dx(0) = 0,
Convert the initial value problem into a set of two coupled
first-order initial value problems
and find the exact solution to the differential equatiion
Consider the following second-order ODE: (d^2 y)/(dx^2 )+2
dy/dx+2y=0 from x = 0 to x = 1.6 with y(0) = -1 and dy/dx(0) = 0.2.
Solve with Euler’s explicit method using h = 0.4. Plot the x-y
curve according to your solution.
Find dy/dx and d^2y/dx^2, and find the slope and concavity (if
possible) at the given value of the parameter. (If an answer does
not exist, enter DNE.)
Parametric
Equations
Point
x = et, y =
e−t
t = 3
dy/dx =
d^2y/dx^2 =
slope =
concavity=
---Select--- concave upward concave downward
neither
1). Find the dervatives dy/dx and d^2/dx^2 , and evaluate them
at t = 2.
x = t^2 , y= t ln t
2) Find the arc length of the curve on the given interval.
x = ln t , y = t + 1 , 1 < or equal to t < or equal to
2
3) Find the area of region bounded by the polar curve on the
given interval.
r = tan theta , pi/6 < or...