Suppose that y1 and y2 form a fundamental pair of solutions of the homogeneous, linear differential equation y"+y'/t+cos(t)y = 0, %3D defined in the interval (0,00). Then the general solution of the equation y"+y'/t+cos(t)y = t %3D is given by ... t ...B· y2 (t) | In(s)yı (s) ds – B · y1 (t) / In(s)y2(s) ds + c1Y1 (t) + c2Y2 (t) where B depends on y, and y2, and c1 and c2 depend on initial conditions. t B. y2 (t) | syı (s) ds – B · y1 (t) | s'y2 (s) ds + ciY1 (t) + c2Y2 (t) ... where B depends on y1 and y2, and c1 and c2 depend on initial conditions. t ..B - y2 (t) / y1 Y1 (s) ds – B · y1 (t)/ ? Y2 (8) ds + c1yı (t) + c2Y2(t) | where B depends on y, and y2, and c1 and c2 depend on initial conditions. O We can't answer this without specific y1 and y2.
Suppose that y1 and y2 form a fundamental pair of solutions of the homogeneous, linear differential equation y"+y'/t+cos(t)y = 0, %3D defined in the interval (0,00). Then the general solution of the equation y"+y'/t+cos(t)y = t %3D is given by ... t ...B· y2 (t) | In(s)yı (s) ds – B · y1 (t) / In(s)y2(s) ds + c1Y1 (t) + c2Y2 (t) where B depends on y, and y2, and c1 and c2 depend on initial conditions. t B. y2 (t) | syı (s) ds – B · y1 (t) | s'y2 (s) ds + ciY1 (t) + c2Y2 (t) ... where B depends on y1 and y2, and c1 and c2 depend on initial conditions. t ..B - y2 (t) / y1 Y1 (s) ds – B · y1 (t)/ ? Y2 (8) ds + c1yı (t) + c2Y2(t) | where B depends on y, and y2, and c1 and c2 depend on initial conditions. O We can't answer this without specific y1 and y2.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Suppose that Y1 and y2 form a fundamental pair of solutions of the homogeneous,
linear differential equation
y"+y'/t+cos(t)y = 0,
defined in the interval (0,0). Then the general solution of the equation
y"+y'/t+cos(t)y = t
is given by...
t
B - y2 (t) .
In(s)y1 (s) ds – ß · y1 (t) | In(s)y2 (s) ds + c1Y1 (t) + c2Y2 (t)
-
where B depends on y, and y2, and c1 and C2 depend on initial conditions.
t
...B. y2 (t)
s y1 (s) ds – B. Y1 (t) | s² y2(s) ds + c1y1 (t) + C2Y2 (t)
where B depends on y1 and y2, and c1 and C2 depend on initial conditions.
- B • y2 (t) |.
Y1 (s) ds – B- yı (t) / Y2(s) ds + c1yı (t) + c2Y2 (t)
where B depends on y, and y2, and c1 and c2 depend on initial conditions.
O We can't answer this without specific y1 and y2.
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