notes 3-4 - y 00-6 y + 9 y = 0. When a constant coecient...

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SECTION 3.4 REPEATED ROOTS AND REDUCTION OF ORDER EXAMPLE. Solve y 00 - 6 y 0 + 9 y = 0. We need another solution to form a fundamental set. A constant times the known solution won’t work. Let’s try v ( t ) y 1 ( t ). For future use, let’s suppose that y 1 ( t ) is a nonzero solution of y 00 + p ( t ) y 0 + q ( t ) y = 0. We’ll use our guess to try to find a y 2 ( t ).
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It’s better not to try to remember formulas, just remember this reduction of order technique for finding a second solution when we already know one. EXAMPLE, CONTINUED. Find a second solution of
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Unformatted text preview: y 00-6 y + 9 y = 0. When a constant coecient dierential equation leads to a repeated root, then multiply the exponential solution by t to get a second solution. EXAMPLE. Find the solution of 16 y 00 + 24 y + 9 y = 0 that satises the initial conditions y (0) = 1, y (0) = 3 / 4. EXAMPLE. Find a fundamental set of solutions of ( x-1) y 00-xy + y = 0 on the interval x > 1, given that y 1 ( x ) = e x is a solution. HOMEWORK: SECTION 3.4...
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notes 3-4 - y 00-6 y + 9 y = 0. When a constant coecient...

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