Math302 M1 EC - y 00 + xf ( x ) y-f ( x ) y = 0 , given...

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Math 302 Midterm Exam Extra Credit Opportunity The following 5 problems are worth up to 10 extra points on the midterm. To get credit for a problem, your solution must be neat, complete, and correct. I will collect your solutions on Monday, April 19. 1. Use reduction of order to find the general solution of x 2 y 00 - xy 0 + y = 0 , given that y 1 = x is a solution. 2. Use reduction of order to find the general solution of y 00 + ( x 2 - 1) y 0 - x 2 y = 0 , given that y 1 = e x is a solution. Your answer should involve an integral. 3. Use reduction of order to find the general solution of
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Unformatted text preview: y 00 + xf ( x ) y-f ( x ) y = 0 , given that y 1 = x is a solution. Here f ( x ) is a arbitrary function. Your answer should involve an integral. 4. Find the general solution of x 2 y 00 + xy-y = x 2 e-x , given that y 1 = x and y 2 = x-1 are solutions of the related homogeneous equation. 5. Find the general solution of 2 x 2 y 00 + 3 xy-y = x-1 , given that y 1 = x 1 / 2 and y 2 = x-1 are solutions of the related homogeneous equation....
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