In Problems 13–32 use variation of parameters to solve the given nonhomogeneous system.
13.
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Chapter 8 Solutions
A First Course in Differential Equations with Modeling Applications (MindTap Course List)
- 11. 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_forward7 -3 [13]. 16 -7 y. Find the general solution of the system y' =arrow_forward7. A scientist places two strains of bacteria, X and Y, in a petri dish. Initially, there are 400 of X and 500 of Y. The two bacteria compete for food and space but do not feed on each other. If x = x(t) and y = y(t) are the numbers of strains at time t days, the growth rates of the two populations are given by the system x' = 1.2x – 0.2y, y' = -0.2x + 1.5y Determine what happens to these two populations by solving the system of differential equations.arrow_forward
- 7. Find the general solution of the given system of equations. (a) (b) y' - [ = -1 3 -2 2 [ y + ex X 2-5 0 y = [² =2] y + [cz] · 1 -2 0 < x < T.arrow_forward9. Form the differential equation of the three-parameter family of conics y = ae* + be2x + ce¬3x where a, b and c are arbitrary constants.arrow_forward1. Solve x' = Ax + b, if A 4 -3 and b 2t -1 -1 -2 2 -18e3t 72e3t 54e3t 2. Solve x' = Ax + b, if A : 2 4 -1 and b 3 3. Find the general solution to the system d 1 2e2t x+ dt -1 4 e3t for 0 2arrow_forward
- 6. What is the general solution of * (x² + 2xy – 4y)dx - (2 – 8xy – 4y)dy = 0 a? - 4y? = c(x - y) x? + 2y = c(x + 2y) O Option 1 O Option 2 a? + 2y? = c(x - 2y) a? + 4y? = c(x + y)arrow_forward19. The solution to (2x – 4y – 3)dy = (x – 2y)dx is: c. 6y +x? + 4xy + 4y? d. 6y +x? – 4xy + 4y? а. бу - х* - 4ху + - 4y? = C b. 6y +x? - 4ху - 4y? = C What is the solution of (2x - y)dx + (4x + y – 6) dy = 0? a. (x+y- 3) = c(2x + y – 4)² b. (x-y+3)² = c(2x + y – 4) ³ 20. c. (x-y-3)° = c(2x – y – 4)² d. (x+y– 3)° = c(x+2y – 4)²arrow_forwardProblem 2. Let dX/dt = AX. Find et and use it to write down the solution to the system. (²2) b) 4-(32) 1 a) A = Aarrow_forward
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