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Welcome to our site! Electro Tech is an online community (with over 170,000 members) who enjoy talking about and building electronic circuits, projects and gadgets. To participate you need to register. Registration is free. Click here to register now.
Q1. The author wants to emphasize that the assumed and soon to be found function u(x) is a solution of the differential equation x²y''-6y=0. That means x≠0. This is important for the reduction of order method.
Q2. The calculated integrating factor is x^6. Multiplying the equation by x^6 will make the left side of the equation into a complete differential. Therefore the solution of the equation is w=c/x^6 . Try substituting it into w'+6w/x = 0 and see.
Q3. The author could have chosen any constant values for c1 and c2 to get y2. Try different values of c1 and c2, then substitute into x²y''-6y=0 and see. He chose those (-5,0) values to get the simplest and lowest degree term value for y2.
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