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  3. 2. consider the system x=3x+4y+etcos(2t),y=2xy+tet

2. Consider the system x=3x+4y+etcos(2t),y=2xy+tet. a) (10 pts) Find the complementary function. b) (10 pts)...

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2. Consider the system x=3x+4y+etcos(2t),y=2xy+tet. a) (10 pts) Find the complementary function. b) (10 pts) What is a "good guess" for a particular solution? c) (10 pts) Find a particular solution. d) (bonus 20pts ) Solve the same system with initial conditions x(0)=y(0)=0 using Laplace transform. You may use a CAS of your choice to do tedious computations (e.g., solve the linear system on X(s) and Y(s) ), however all the key steps must be present in your solution. 2. Consider the system x=3x+4y+etcos(2t),y=2xy+tet. a) (10 pts) Find the complementary function. b) (10 pts) What is a "good guess" for a particular solution? c) (10 pts) Find a particular solution. d) (bonus 20pts ) Solve the same system with initial conditions x(0)=y(0)=0 using Laplace transform. You may use a CAS of your choice to do tedious computations (e.g., solve the linear system on X(s) and Y(s) ), however all the key steps must be present in your solution

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