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Unformatted text preview: Example
Solve the separable diﬀerential equation
dy sin x − 4y cos2 x
subject to the initial condition y π
3 dx = 0, = 1. First separate variables:
dx sin x − 4y cos2 x sin x
cos2 x 4y dy = then integrate both sides (using the substitution u = cos x):
cos2 x 4y dy =
2y 2 = − du
u2 y2 = 1
2 cos x y2 = 1
sec x + C.
2 Solving for the constant C using the initial condition y
y2 = ⇒ π
3 = 1 leads to 1 − 1 = C, 1
2 Solving for y explicitly
2 and using the initial condition, the solution is
y ( x) = 1
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This note was uploaded on 04/02/2012 for the course MTH 132 taught by Professor Kihyunhyun during the Fall '10 term at Michigan State University.
- Fall '10