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solve the differential equation (D^2+a^2 )y=cos ax
Q:

solve the differential equation (D^2+a^2 )y=cos ax

hamza
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2022-05-18
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solve the differential equation
 (D^2+a^2 )y=cos ax

Mathematics,
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hamza
2022-05-18
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Here the  A.E. is                        m^2+a^2=0    
i.e.                                              m=±ia
so
Y_(C.F.)=c_1  cos⁡ax+c_2  sin⁡ax
Y_(P.I.)=1/(D^2+a^2 )  cos⁡ax=x/2a  sin⁡ax   (Remark)
Then,
Y_(G.S.)=c_1  cos⁡ax+c_2  sin⁡ax+x/2a  sin⁡ax

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hamza
2022-05-18
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hamza
2022-05-18
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