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In Problems 13–32 use variation of parameters to solve the given nonhomogeneous system.
17.
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A First Course in Differential Equations with Modeling Applications (MindTap Course List)
- 2.2. Solve the following initial value problems: a) t+2y=², y(2)=1. b) c) "+y=0, y(0)=1, (0) = -2. + 2y +2y=0, (0)=2, (0) = 1.arrow_forwardExample 2: Find the particular solution of (x – y)dx + (3x+y)dy = 0 when x = 2 & y = -1.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_forward
- 1. The Lotka-Volterra or predator-prey equations dU = aU – UV, dt (1) AP = eyUV – BV. dt (2) have two fixed points (U., V.) = (0,0), (U., V.) = (- :). The trivial fixed point (0,0) is unstable since the prey population grows exponentially if it is initially small. Investigate the stability of the second fixed point (U..V.) = 6:27 PM 3/3/2021 近arrow_forwardIn Problems 1–8 use the method of undetermined coeffi cients to solve the given system. dx 1. = 2x + 3y – 7 dt dy 2у + 5 = -x - dt dx 2. dt 5х + 9у + 2 dy — —х + 11у +6 dt -G )x+ (,) 3 3. X' = 3 t (4t + 9er\ 4. X' = 4 -4 х+ 1 -t + e6t 3 X + le' 10 5. X' = sin t 5 X + 1 6. X' 1 -2 cos 7. X' = 2 3 X +| -1 \0 0 5, 2 8. X' = 5 0 ]X + - 10 5 0 0/ 40/arrow_forward7 -3 [13]. 16 -7 y. Find the general solution of the system y' =arrow_forward
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