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)
- 3. 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_forward4. 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_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
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- Question 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_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_forwardTwo very large tanks A and B are partially filled with 100 gallons of brine each. Initially, 100 pounds of salt are dissolved in the solution in tank A and 50 pounds of salt are dissolved in the solution in tank B. The system is closed, since the well-mixed liquid is pumped only between the tanks as shown in the figure. 1. Use the information in the figure to construct a mathematical model for the number of pounds of salt x1(t) and x2(t) at time "t" in tanks A and B, respectively. 2. Find a relationship between the variables x1(t) and x2(t) that holds at time «t». 3. Explain why this relationship makes intuitive sense. 4. Use this relationship to help find the amount of salt in tank B at t = 30 min.arrow_forward
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