6. Solve the system of first order differential equations: x'(t) = X1 + X2 x2(t)x 3x2 6. Solve the system of first order differential equations: x'(t) = X1 + X2 x2(t)x 3x2
6. Solve the system of first order differential equations: x'(t) = X1 + X2 x2(t)x 3x2
10. Use variation of parameters to solve the system of first order differential equations: x1(t) = 2x1-12 10. Use variation of parameters to solve the system of first order differential equations: x1(t) = 2x1-12
Calculate the solution x(t) = (n(t), P2(t),T3(t)) of the system of differential equations X1 = X2 + X3 x3 = x1 + x2 subject to the following initial conditions: Calculate the solution x(t) = (n(t), P2(t),T3(t)) of the system of differential equations X1 = X2 + X3 x3 = x1 + x2 subject to the following initial conditions:
Along with x1' please solve for x2'. Thanks! Transform the given differential equation into an equivalent system of first-order differential equations. y' (t) + 5y' (t) - 6ty(t) = 6 cost Let x, = y and X, Ey. Complete the differential equation for X.
Solve the following system of first order differential equations: Given the system of first-order differential equations ()=(3) () determine without solving the differential equations, if the origin is a stable or an unstable equilibrium. Explain your answer.
l c The amounts x1 (t) and x2 (t) of salt in two brine tanks satisfy the differential equations below where ki = for i= 1. 2. The volumes are V,-50 (gal) and v2-25 (gal). First solve for x1(t) and x2(t) assuming that r#20 (gai in). x1(0): 25(b), and x2(0)-Ο Then find the maximum amount of salt ever in tank 2 Finally, construct a figure showing the graphs of x,(t) and x2t) dx1 dx2 l c The amounts x1 (t)...
Consider the linear system of first order differential equations x' = Ax, where x= x(t), t > 0, and A has the eigenvalues and eigenvectors below. 4 2 11 = -2, V1 = 2 0 3 12 = -3, V2= 13 = -3, V3 = 1 7 2 i) Identify three solutions to the system, xi(t), xz(t), and x3(t). ii) Use a determinant to identify values of t, if any, where X1, X2, and x3 form a fundamental set of...
10. Solve the system of differential equations by using eigenvalues and eigenvectors. x1 = 3x, + 2x2 + 2xz x2 = x + 4x2 + x3 X;' =-2x, - 4x2 – x3
Step by step please. Solve the system of first-order linear differential equations. (Use C1 and C2 as constants.) Yı' = y1 Y2' = 3y2 (y1(t), yz(t)) = ) x Solve the system of first-order linear differential equations. (Use C1, C2, C3, and C4 as constants.) Yi' = 3y1 V2' = 4Y2 Y3' = -3y3 Y4' = -474 (71(t), yz(t), y(t), 74(t)) =
(1 point) xi(t) Let x(t) = be a solution to the system of differential equations: x2(t) xy(t) x'z(t) –6 x (1) 2 xi(t) x2(t) 3 x2(t) = If x(0) find x(t). 2 3 Put the eigenvalues in ascending order when you enter xi(t), x2(t) below. xi(t) = exp( t)+ expo t) x2(t) = exp( t)+ expl t)