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Unformatted text preview: y1(t) and y2(t). This means that
ay1 + by1 + cy1 = 0 and
ay2 + by2 + cy2 = 0 Homog. eq. with constant coeff. (Section 3.1)
ay + by + cy = 0
• Suppose you already found a couple solutions, y1(t) and y2(t). This means that
ay1 + by1 + cy1 = 0 and
ay2 + by2 + cy2 = 0 • Notice that y(t) = C1y1(t) is also a solution. Plug it in and check: Homog. eq. with constant coeff. (Section 3.1)
ay + by + cy = 0
• Suppose you already found a couple solutions, y1(t) and y2(t). This means that
ay1 + by1 + cy1 = 0
ay2 + by2 + cy2 = 0 and • Notice that y(t) = C1y1(t) is also a solution. Plug it in and check: a(C1 y1 ) + b(C1 y1 ) + c(C1 y1 )
Homog. eq. with constant coeff. (Section 3.1)
ay + by + cy = 0
• Suppose you already found a couple solutions, y1(t) and y2(t). This means that
ay1 + by1 + cy1 = 0
ay2 + by2 + cy2 = 0 and • Notice that y(t) = C1y1(t) is also a solution. Plug it in and check: a(C1 y1 ) + b(C1 y1 ) + c(C1 y1 )
= aC1 (y1 ) + bC1 (y1 ) + cC1 (y1 )
Homog. eq. with constant coeff. (Section 3.1)
ay + by + cy = 0
• Suppose you already found a couple solutions, y1(t) and y2(t). This means that
ay1 + by1 + cy1 = 0
ay2 + by2 + cy2 = 0 and • Notice that y(t) = C1y1(t) is also a solution. Plug it in and check: a(C1 y1 ) + b(C1 y1 ) + c(C1 y1 )
= aC1 (y1 ) + bC1 (y1 ) + cC1 (y1 )
= C1 (ay1 + by1 + cy1 ) Homog. eq. with constant coeff. (Section 3.1)
ay + by + cy = 0
• Suppose you already found a couple solutions, y1(t) and y2(t). This means that
ay1 + by1 + cy1 = 0
ay2 + by2 + cy2 = 0 and • Notice that y(t) = C1y1(t) is also a solution. Plug it in and check: a(C1 y1 ) + b(C1 y1 ) + c(C1 y1 )
= aC1 (y1 ) + bC1 (y1 ) + cC1 (y1 )
= C1 (ay1 + by1 + cy1 ) = 0 Homog. eq. with constant coeff. (Section 3.1)
• Which of the following functions are also solutions?
(A) y(t) = y1(t)2
(B) y(t) = y1(t)+y2(t)
(C) y(t) = y1(t) y2(t)
(D) y(t) = y1(t) / y2(t) Homog. eq. with constant coeff. (Section 3.1)
• Which of the following functions are also solutions?
(A) y(t) = y1(t)2
(B) y(t) = y1(t)+y2(t)
(C) y(t) = y1(t) y2(t)
(D) y(t) = y1(t) / y2(t) Homog. eq. with constant coeff. (Section 3.1)
• Which of the following functions are also solutions?
(A) y(t) = y1(t)2
(B) y(t) = y1(t)+y2(t)
(C) y(t) = y1(t) y2(t)
(D) y(t) = y1(t) / y2(t)
• In fact, the following are all solutions: C1y1(t), C2y2(t), C1y1(t)+C2y2(t). Homog. eq. with constant coeff. (Section 3.1)
• Which of the following functions are also solutions?
(A) y(t) = y1(t)2
(B) y(t) = y1(t)+y2(t)
(C) y(t) = y1(t) y2(t)
(D) y(t) = y1(t) / y2(t)
• In fact, the following are all solutions: C1y1(t), C2y2(t), C1y1(t)+C2y2(t).
• With ﬁrst order equations, the arbitrary constant appeared through an
integration step in our methods. With second order equations, not so...
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 Spring '13
 EricCytrynbaum
 Differential Equations, Equations

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