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## Main Question or Discussion Point

What is the logic behind equating differential equations to zero? For example the equation

y''-5y'+6y=0

Because it can just as easily be written y''-5y'=-6y

I am interested in the meaning of why if we sum y''+(-5y')+6y equals zero. What is the relationship of its second derivative, first derivative, and 6y?

y''-5y'+6y=0

Because it can just as easily be written y''-5y'=-6y

I am interested in the meaning of why if we sum y''+(-5y')+6y equals zero. What is the relationship of its second derivative, first derivative, and 6y?