Question: vector space, matrix, differential equation

       

Let V be the vector space consisting of all functions of the form
αe2xcos(x)+beta*e*2*x*sin(x)
 
Consider the following linear transformation L : V → V :
L(f) = f' +f
 
(a) Find the matrix representing L with respect to the basis {e2xcos(x),e2xsin(x)}
 
 
(b) Use your answer from part (a) to find one solution to the following differential equation :                                                                      
 
y'+y= e^2*x*cos(x)

 

 

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