In Problems 13–32 use variation of parameters to solve the given nonhomogeneous system.
13.
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Chapter 8 Solutions
Bundle: A First Course in Differential Equations with Modeling Applications, Loose-leaf Version, 11th + WebAssign Printed Access Card for Zill's ... Problems, 9th Edition, Single-Term
- 6. (2x +3y = 0 /2x x+2y =-1 9. (1 1 -X+-y 5 1, -x+y%3D10 4arrow_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
- 5. Find a general solution of the linear system. x' = 2x + y ly' = x + 2y – e2tarrow_forward9. discuss the behavior of the dynamical system Xk+1= Axk where -0.31 (@) A = [ (b) A = ["0.3 11 1.5 0.3 (b) A = 0.3 1 3Darrow_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
- 9. 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_forwardEx.3 pleasearrow_forward7. 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_forward
- 5. Find the general solution of (D³-D)y=4e*+3ex. Ans. y=2xe*+(1/2)e2+c1+c2e*+c3e*arrow_forward6. 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_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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