2) Show that y = A cos x + Bsin x, where A and B are constants, is a general solution of the differential equation d²y + y = 0 dx2 Hence, find the solution of this equation subject to the following boundary conditions y(0) = 1, yGr) = 1

Elements Of Electromagnetics
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Author:Sadiku, Matthew N. O.
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2) Show that y = A cos x + Bsin x, where A and B are constants, is a general solution of the
differential equation
d²y
+ y = 0
dx2
Hence, find the solution of this equation subject to the following boundary conditions
y(0) = 1,
= 1
(cos, sin)
S
A
Unit Circle
sin
tan =
Quadrant II:
cos
Quadrant I:
- +
+
(0, 1)
2'2
2
2'2
90°
120°
60°
4
135°
45°
150°
30°
180°
0°
(-1,0)
(1, 0)
360°
210°
330°
117
6
(목)
225°
315°
240°
300°
4
270°
3
2
2
2
(0, –1)
C
Quadrant Ill:
Quadrant IV:
프_3
Transcribed Image Text:2) Show that y = A cos x + Bsin x, where A and B are constants, is a general solution of the differential equation d²y + y = 0 dx2 Hence, find the solution of this equation subject to the following boundary conditions y(0) = 1, = 1 (cos, sin) S A Unit Circle sin tan = Quadrant II: cos Quadrant I: - + + (0, 1) 2'2 2 2'2 90° 120° 60° 4 135° 45° 150° 30° 180° 0° (-1,0) (1, 0) 360° 210° 330° 117 6 (목) 225° 315° 240° 300° 4 270° 3 2 2 2 (0, –1) C Quadrant Ill: Quadrant IV: 프_3
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