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manzneedshelp

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Could someone please provide guidance on how to begin this problem? I've attached the preface to the assignment question.Show that the general solution of the differential equation

y″(x)=−y(x)

is

y(x)=Acos(x)+Bsin(x)

where A and B are arbitrary constants. Hint: You'll need the Taylor series representations for sin and cos.View attachment 8274

y″(x)=−y(x)

is

y(x)=Acos(x)+Bsin(x)

where A and B are arbitrary constants. Hint: You'll need the Taylor series representations for sin and cos.View attachment 8274