Solve the given system of differential equations by systematic elimination. 2 dx/dt − 4x + dy dt = et dx/dt − x + dy dt = 3et
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.
Solve the given initial value problem. x(0) = 1 dx = 4x +y- e 3t, dt dy = 2x + 3y; dt y(0) = -3 The solution is X(t) = and y(t) =
Find dy for the given values of x and Ax. y = 4x? - - 9x; * = - 3 and Ax=0.3 (Round to the nearest tenth as needed.) Enter your answer in the answer box MacBook esc F 90 F a # 1 2 3 $ 4 % 5 6 & 7 Q W IT R T Y A S C L
dy Find the function y(x) satisfying dx = 4x - 9 and y(5) = 0. dy The function y(x) satisfying = 4x - 9 and y(5)= 0 is y(x) = dx
(a) Find the derivative. y = In(4x – 5) – 3 In(x) dy dx (b) Find the derivative. 4x - y = = In dx State whether the function in part (b) is the same function as that in part (a). The function in part (b) is the same function as that in part (a). The function in part (b) is not the same function as that in part (a).
Given y=f(u) and u=g(x), find dy/dx y=u^2, u=4x-5
Consider the following system. dx dt dy dt 5 x + 4y 2 3 =X - 3y 4 Find the eigenvalues of the coefficient matrix Alt). (Enter your answers as a comma-separated list.) Find an eigenvector for the corresponding eigenvalues. (Enter your answers from smallest eigenvalue to largest eigenvalue.) K K₂ = Find the general solution of the given system. (x(t), y(t)) =
3) For the given system restrict attention to the first quadrant, (x, y = 0). dx x(-4x – y +160) dt dy = y(-12 - y2 + 2500) dt Find and classify all equilibria.
Find the solution to the given systems
(a) X'=X
X(0)=
(b) dx/dt=5x+y dy/dt=-2x+3y
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