Problem #7: Let L(y)=an​y(n)(x)+an−1​y(n−1)(x)+⋯+a1​y′(x)+a0​y(x) where a0​,a1​,…,an​ are fixed constants. Consider the

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Problem 7 Let L Y An Y N X An 1 Y N 1 X A1 Y X A0 Y X Where A0 A1 An Are Fixed Constants Consider The 1 (69.97 KiB) Viewed 33 times

Problem #7: Let L(y)=an​y(n)(x)+an−1​y(n−1)(x)+⋯+a1​y′(x)+a0​y(x) where a0​,a1​,…,an​ are fixed constants. Consider the nth order linear differential equation L(y)=6e2xcosx+3xe2x(∗) Suppose that it is known that L[y1​(x)]=5xe2x when y1​(x)=10xe2x L[y2​(x)]=9e2xsinx when y2​(x)=72e2xcosx L[y3​(x)]=9e2xcosx when y3​(x)=18e2xcosx+90e2xsinx Find a particular solution to (∗). Enter your answer as a symbolic function of x, as in these Do not include ' y= ' in your answer. Problem #7: examples Problem #8: Solve the following initial value problem. y(4)−6y′′′+5y′′=4x,y(0)=0,y′(0)=0,y′′(0)=0,y′′′(0)=0 Enter your answer as a symbolic function of x, as in these