5) Both x andy denote functions of t that are Irelated by the given equation. x²...
Assume that x and y are both differentiable functions of t and are related by the equation 42 y= 22 +3 Find dy when 2 = 0, given dt de dt 2 when x = 0 Enter the exact answer. 11 dt
Assume that x and y are functions of t, and x and y are related by the equation y= 4x+3. (a) Given that dx/dt=1, find dy/dt when x=2. (b) Given that dy/dt=4, find dx/dt when x=3.
Suppose y = √(2x + 1), where x and y are functions of t. (a) If dx/dt = 3, find dy/dt when x = 4 (b) If dy/dt = 4, find dx/dt when x = 40.
1. Determine if the differential equation x^2y′=y(x+y) is homogeneous or Bernouilli or both. Give a solution using any method that applies. 2. Solve the differential equation y′= 2x(y+y^2) using the method of Bernouilli equation. Also give a solution for the same differential equation using the method of separable DE. 3. Consider the differential equation y′′= (y′)^2. It is has both x and y variable missing.Give solutions to the DE using the two different methods corresponding t ox-variable missing, and y-variable...
Ox = C1e3t Find the general solution to the given system. de = 1 = 1 + 2y dy = 2x + y None of these 0x = Cie3t+cze- y=3c1e3+ + cze- y=cie3+ + 3c2e-t -t - Ox 2 = caeht Czert y=-cie3+ + 3c2e-t -t +cze Ox = cie3t y = cie + 3c2e-
Find the particular solution to the given differential equation that satisfies the given conditions. d2y 9 dy 14y= 12 - ex; 4) dx dx2 and y - 29 when x = 0 42 dy dx 2 2x A) y B) y 7 6 7 6 사우-등나을이건을. 22x+ 27x-6_1 ex 2 2x-2,7x,6_1 5 7 6 C) y D) y 7 6 Find the particular solution to the given differential equation that satisfies the given conditions. d2y 9 dy 14y= 12 -...
1. -/5 POINTS LARCALC11 2.6.003. 0/2 Submissions Used Assume that x and y are both differentiable functions of t and find the required values of dy/dt and dx/dt. y = x (a) Find dy/dt, given x = 1 and dx/dt = 8. dy/dt = (b) Find dx/dt, given x = 64 and dy/dt = 7. dx/dt =
Prob.II. Differentiate the following functions, and simplify. 1. f(x) 2x-3 x+4 2. f(x) = x²(x - 2)* 3. f(x) = In (x V1 - x2) 4. f(x) = x2e-* 5. Find dy/dx = y' for the equation x2 + y2 = 25 and find y" (check H.W)
Solve the equation for u(x, t) if it satisfies the equation: with boundary and initial conditions given by where δ(x) and δ(t) are Dirac delta functions. 2. du-Ka_ = δ(x-a)s(t) for 0 < x < oo; t > 0 at ах? du ах (0, t) = 0;u(co, t) =0;(mt) = 0; u(x, 0)=0 ox Solve the equation for u(x, t) if it satisfies the equation: with boundary and initial conditions given by where δ(x) and δ(t) are Dirac delta functions....
Find the equation of the plane that contains both the line with the equation x = 3 + 2t,y = t , z 8-t, and the line with the equation x = 5 + t,y = 4-t,z = 6 Find the equation of the plane that contains both the line with the equation x = 3 + 2t,y = t , z 8-t, and the line with the equation x = 5 + t,y = 4-t,z = 6