In Problems 1–8 use the method of undetermined coefficients to solve the given nonhomogeneous system.
1.
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A First Course in Differential Equations with Modeling Applications (MindTap Course List)
- 4. Solve the system dt -1 with a1 (0) = 1 and 2(0) = -1.arrow_forward11. What is the general solution of* (2x – y)dx + (4x + y - 6)dy = 0 (2 +y – 3) = c(2x + y - 4)2 (x – y + 3)? = c(2æ + y – 4)3 Option 1 Option 2 (2 - y - 3) = c(2r - y- 4) (x+y - 3) = c(x + 2y – 4)?arrow_forward3. 2хydx - (3xу + 2y?)dy %3D0 o (x - 2y)*(2x +y) = c (х — у)"(х + у) %3 с (х + 2y) (2х- у)* %3 с (x – 2y)* = c(2x + y)arrow_forward
- 6. (2x +3y = 0 /2x x+2y =-1 9. (1 1 -X+-y 5 1, -x+y%3D10 4arrow_forward4. (S.10). Use Gaussian elimination with backward substitution to solve the following linear system: 2.r1 + 12 – 13 = 5, 1 + 12 – 3r3 = -9, -I1 + 12 +2r3 = 9;arrow_forward13 Solve the following linear system of DE; x' = Añ. 9x15x2 + 3x3 4x2 + 3x3 O 13arrow_forward
- a " OMANTEL If E (X) = -2 and V(X) = 6 () Е(5X — 2) 3 5 E(X) — Е(2) — (5x (-2)) — 2 %3D -12 (iї) V(5X — 2) %3D 52 V(X) — V(2) 3 (25 х 6) — 0 %3D150 (iї) V(-5X — 2) %3D (-5)?V(X) — V(2) 3D (25 х 6) —0 %3D 150 (iv) E (X²) =?arrow_forward3. Simple pulley system gives the equations X1 = T - g 2x2 = T – 2g X1 + x2 = 0 (a) Determine X1, X2 and T if g = 10 (b) Verify your solutions using Gaussian eliminationarrow_forwardUse (1) in Section 8.4 X = eAtc (1) to find the general solution of the given system. 1 X' = 0. X(t) =arrow_forward
- .The system x′=3(x+y−13x3−k),y′=−13(x+0.8y−0.7)x′=3(x+y−13x3−k),y′=−13(x+0.8y−0.7) is a special case of the Fitzhugh–Nagumo16 equations, which model the transmission of neural impulses along an axon. The parameter k is the external stimulus. a.Show that the system has one critical point regardless of the value of k.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_forwardQuestion 9 Find all the roots of z3 – 3(5 +j) = 0 and give the answers in rectangular form. Question 10 Use Crammer's rule to solve the following linear system for y only. 2x – 3y = 3 – z 4x +y = -4 = 3y + z-2 İLIFE Digitalarrow_forward
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