Find dy/dx and d2y/dx2 ? x = t2 + 9, y = t2 + 5t For which values of t is the curve concave upward? (Enter your answer using interval notation.)
38. [-13 Points] DETAILS SCALCET8 10.2.011. Find dy/dx and dạy/dx2. x = +2 + 9, y = t2 + 5t dy dx dy ho = dx² For which values of t is the curve concave upward? (Enter your answer using interval notation.)
(1 point) Let a be a real constant. Consider the equation dx2 dx with boundary conditions y(0)0 and y(2) 0 For certain discrete values of a, this equation can have non-zero solutions. Find the three smallest values of a for which this is the case. Enter your answers in increasing order. a2 , аз Note: You can earn partial credit on this problem (1 point) Let a be a real constant. Consider the equation dx2 dx with boundary conditions y(0)0...
Calculate dzy dx2 y = -x + et dey dx2 = Calculate dzy dx2 y = 7 x2 day dx2 = The graph of a function is given. Find the approximate coordinates of all points of inflection of the function (if any). (If there are no inflection points, enter DNE.) (x, y) = (smaller x-value) (x, y) = (larger x-value) y w х
Solve the following differential equations x2d2y/dx2 − xdy/dx − 3y = lnx/ x , x > 0. show that the answer is y = A/x + Bx3 − lnx/ 6x (2lnx + 1) x d2y/dx2 − dy/dx + 2y/x = (ln x)2 .show that the answer is y = x { A cos(ln x) + B sin(ln x) + (lnx) 2 − 2 }
Problem #3 Solve initial value problem as follows: 1 r2 dạy dy + 4x dx2 dx + 2 y = y|x=1 dy dx = 2, | x=1 = 3. х dy Calculate the value of at the point where x = 2, round-off your value of the derivative to four figures and dx present your result below (10 points): (your numerical result for the derivative must be written here)
dy dy dx2 dx tycos(ox 8) Solve: 47+d7+y - cos(ox) Find the amplitude of the steady-state solution (after transients have died down) in terms of w. The find the value of that makes the amplitude as large as possible. dy dy dx2 dx tycos(ox 8) Solve: 47+d7+y - cos(ox) Find the amplitude of the steady-state solution (after transients have died down) in terms of w. The find the value of that makes the amplitude as large as possible.
Find the derivative of the function, NI y=-5(-9x² + 2x) فيا انا dy dx 25( - 9x2 + 2x) -(-18x+2) 2 > > Enter your answer in the answer box A hp
Evaluate the following integral. 10-100 -, x> 10 Nx? - 100 dx S = 1x2-100 Enter your answer in the answer box javascript:doExercise (5);
4. Consider the homogeneous differential equation dy d y dy-y=0 dx3 + dx2 dx - y (a) Show that 01 (C) = e is a solution. (b) Show that 02 (2) = e-* is a solution. (c) Show that 03 (x) = xe-" is a solution. (d) Determine the general solution to this homogeneous differential equation. (e) Show that p (2) = xe" is a particular solution to the differential equation dy dy dy dx3 d.x2 - y = 4e*...