In Problems 35–46 find the general solution of the given system.
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FIRST COURSE IN DIFF.EQ.-WEBASSIGN
- 13 Solve the following linear system of DE; x' = Añ. 9x15x2 + 3x3 4x2 + 3x3 O 13arrow_forward5. Find the general solution of the given system. X' = [; x. Х.arrow_forward5. The following sets of simultaneous equations may or may not be solvable by the Gaussian Elimination method. For each case, explain why. If solvable, solve. (a) (b) (c) (d) x+y+3z=5 2x + 2y + 2z = 14 3x + 3y+9z = 15 2 -1 1] 4 1 3 2 12 3 2 3 16 2x-y+z=0 x + 3y + 2z=0 3x + 2y + 3z == 0 x₁ + x₂ + x3-X₂ = 2 x1-x₂-x₂ + x₁ = 0 2x₁ + x₂-x3 + 2x4 = 9 3x₁ + x₂ + 2x3-X4 = 7arrow_forward
- Section 2.2 2.1. Solve the following difference equations: (a) Yk+1+Yk = 2+ k, (b) Yk+1 – 2Yk k3, (c) Yk+1 – 3 (d) Yk+1 – Yk = 1/k(k+ 1), (e) Yk+1+ Yk = 1/k(k+ 1), (f) (k + 2)yk+1 – (k+1)yk = 5+ 2* – k2, (g) Yk+1+ Yk = k +2 · 3k, (h) Yk+1 Yk 0, Yk = ke*, (i) Yk+1 Bak? Yk (j) Yk+1 ayk = cos(bk), (k) Yk+1 + Yk = (-1)k, (1) - * = k. Yk+1 k+1arrow_forwardFind the real-valued general solution to the following systems of equations 2 -5 x'(t) = ({arrow_forwardIf the given solutions 2 – 2t yi(t): y2(t) = 2t form a fundamental set (i.e., linearly independent set) of solutions for the initial value problem 21-2 1– 21-1 + 21-2 -23 y, y(3) = t > 0, y -2t-2 2t-1 – 21-2 -34 impose the given initial condition and find the unique solution to the initial value problem for t > 0. If the given solutions do not form a fundamental set, enter NONE in all of the answer blanks. 2t 0) = At) = ( + ( 2tarrow_forward
- 1.4 Consider the system x + 2y + 3z = a 2x + 5y + (a + 5)z = -2 + 2a -y + (a² – a)z = a² – a Find (if possible) the values of a for which the system has (a) No solution (b) Exactly one solution (c) Infinitely many solutionsarrow_forwardQuestion 5. Score: 0/1 If the system 6x 2x 14x + 5z 8y 6z = 28y + hz = 4y + = has infinitely many solutions, then k = ४ 4 8 k OF and h =arrow_forwardProblem 2 Show whether the two equations y₁ = 12e and y2 = 1.2e are independent or dependent using the Wronskian.arrow_forward
- III. Solve the following linear systems of differential equations. dr₁ dt (a) (b) dx2 dt dx₁ dt dx₂ dt = x1 + 2x₂ = = = 4x1 + 3x2 x₁ - 4x₂ 4x₁ - 7x₂ (c) (d) dx₁ dt dx₂ dt dx₁ dt dx₂ dt = -4x1 + 2x2 = = = 5 2²1 +22 -2x1 - 2x₂ 2x16x₂ X(0) = [-2] X(0) = [1¹]arrow_forward1arrow_forwardSolve the following system -3 2 -5 3 X2 X1 dt X2 sin(t) cos(t) 3/2cos(t) + 1/2sin(t)| X1 + c2 /2sin(t)-1/2cos(t)] = C1 X2 B cos(t) sin(t) X1 3cos(t) - sin(t) + 3sin(t) + cos(t) cos(t) 3/2sin(t) – 1/2cos(t) sin(t) + 3/2cos(t) +1/2sin(t) X1 = C1 X2 sin(t) 3/2sin(t) +1/2cos(t) cos(t) - 3/2cos(t) – 1/2sin(t) X1 +c2 = C1 X2arrow_forward
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