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find the general solution for 14,15,16
differential equation
14. z't) 1 -5 21) =(0) 15. z'(t) = 10 0 2 1 -2 (t) 3 2 -1 16. x'(t) = -3 0 2 1 -1 0 (t) -2 -1 0 Recall: Given two functions f(t) and g(t), which are differentiable on an interval I, • If the Wronskian W(8,9)(to) #0 for some to El, then f and g are linearly independent for all t E I. If f(t) and g(t) are...
This is a differential equations course, please answer all the
questions.
Find the general solution.
14. '(t) = (+5 -1)=(1) 15. z'(t) '10 0 21 -2 (1) 3 2 -1 16. z'(t) = -30 2 1 -1 0 (t) -2 - 1 -1 0
Find the general solution of the given system. 5 -1 2 -1 0 5 x(t) = eBook
Find the general solution of the given system. 5 -1 2 -1 0 5 x(t) = eBook
z(t) y(t) 2 0 (22 points) Find the general solution to3"(1)-Ax(t), where A = | 1-2 | , and i(t)-
Find the general solution of the given system. = x + y - Z - z (x(t), y(t), z(t)) =
1.Find a general solution to the given differential equation. 21y'' + 8y' - 5y = 0 A general solution is y(t) = _______ .2.Solve the given initial value problem. y'' + 3y' = 0; y(0) = 12, y'(0)= - 27 The solution is y(t) = _______ 3.Find three linearly independent solutions of the given third-order differential equation and write a general solution as an arbitrary linear combination of them z"'+z"-21z'-45z = 0 A general solution is z(t) = _______
FIND THE GENERAL SOLUTION
Need ALL 4. Differential Equations class
13. x(t) E) (1) 2) st) 14. 7'(t) = ( 1 5 0 15. 7'(t) = ( 2 1 32 0 -20 x(t) - 1 16. 7'(t) = 3 0 2 1 -10 | z(t) -2 -1
5. Find the general solution of the inhomogeneous equation ty"- (t +1)y+y given that 1 (t) e 2 (t) t+1
FIND THE GENERAL SOLUTION
Need ALL 4. Differential Equations class
1 1 2 5. x'(t) = (1 2 1 2 1 6. x'(t) = 2 -8 -5 -1 *(t) -3 3 2 4 7. x'(t) = (2 0 2 2 0 2 *(t) 4 2 3 1 8. x'(t) = 2 4 -1 -1 3 2 z(t) 1
Find a general solution to the given equation for t<0. y''(t) – Ły'(t) + 5 -y(t) = 0 t The general solution is y(t) = (Use parentheses to clearly denote the argument of each function.)