Method of Undetermined Coefficients?
2015-03-09 7:32 pm
Using the Method of Undetermined Coefficients, solve the equation y′′+16y=e^2x where y(0)=y′(0)=0.
回答 (1)
2015-03-11 12:44 am
general solution
y'' + 16 y = 0
y_g = C_1 sin 4x + C_2 cos 4x
suppose y_p = A e^2x
y'' = 4 A e^2x
y'' + 16y = 20 A e^2x
A = 1/20
y = C_1 sin 4x + C_2 cos 4x + 1/20 e^2x
y(0) = C_2 + 1/20
C2 = -1/20
y = C_1 sin 4x - 1/20 cos 4x + 1/20 e^2x
y' (0) = 4 C_1 + 2/20 = 0
C_1 = - 1/80
y = -1/80 sin 4x - 1/20 cos 4x + 1/20 e^2x
y'' + 16 y = 0
y_g = C_1 sin 4x + C_2 cos 4x
suppose y_p = A e^2x
y'' = 4 A e^2x
y'' + 16y = 20 A e^2x
A = 1/20
y = C_1 sin 4x + C_2 cos 4x + 1/20 e^2x
y(0) = C_2 + 1/20
C2 = -1/20
y = C_1 sin 4x - 1/20 cos 4x + 1/20 e^2x
y' (0) = 4 C_1 + 2/20 = 0
C_1 = - 1/80
y = -1/80 sin 4x - 1/20 cos 4x + 1/20 e^2x
收錄日期: 2021-04-15 18:45:28
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https://hk.answers.yahoo.com/question/index?qid=20150309113256AAHoEBB