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(2) (4 marks.) Find the general solution of the ODE e-2x Y"' + 4y + 4y...
For #1 and #2, find the general solution of the ODE system tX' = AX, t> 0. (You do NOT need to verify that the Wronskian is nonzero.) 1. A= ( 1)
First-Order ODE (a) .Find the general solution of the following ODE: (b). Find the general solution (for x > 0) of the ODE : Hint: try the change of variables u ≜ x, v ≜ y/x. (c). Find the solution to the ODE that satisfies y(2) = 15. Hint: Try separation of variables. For integration, try partial fraction decomposition. 2Ꮖy 2 Ꭸ , . + <+5 12 , fi - z - ,fix = zu y' = y2...
2. a) Solve the initial value problem dy 1 dx 1+2x y -2x+1:y(2)-5 b) Explain why this solution is defined for all x >-
2 a) Find the particular solution for y' - 2y' + y = 6e' b) Find y, for y' + 3y' - 36x² + 8e-> JT JT c)Find the general solution y(x) = y, + Ay, (x) + Byz(x),and solve IV y + 4y = 2 sin2t, y
Q1 (7 points) For k e R any constant, find the general solution to xa y" + (1 – k)x y' = 0, and use it to show that when k < 0, all solutions tend to a constant as x + 2O.
Classify each equation as linear or nonlinear dy/dx = y^3 - 9 linear y" = 3y' - 6 nonlinear > 3y y' = 6-4 linear > 4x^2 y" - 3x y' + 4y = 2x - 4 linear
(1 point) Find the general solution, y(t), which solves the problem below, by the method of integrating factors. 6t+y=t", t> 0 dt Put the problem in standard form. Then find the integrating factor, y(t) = and finally find y(t) = (use C as the unkown constant.)
Please explain in with detail Use the substitution y = x' to find a general solution to the given equation for x>0. x?y''(x) + 12xy'(x) + 29y(x) = 0 2 2 - 11-15 - 11+5 tax (Type an exact answer, using radicals as needed.) y(x) = CX
Q1: Find the general solution to the ODE: y'' + 4y' + 13y = 0.
U Question 22 1 pts Find the absolute minimum of f(x, y) = x2 + 4y? - 2x²y + 4 on the square given by -1 << < 1 and -1<y<1. 11 4 8 None of the above or below O-2 07