Solve the differential equation? 2dy/dx-y=e^x/2 .

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Answer 1 · 2018-06-10T18:06:26

#y=1/2xe^(x/2)+Ce^(x/2)#

#2(dy)/(dx)-y=e^(x/2)#

#=>(dy)/(dx)+(-1/2)y=1/2e^(x/2)--(1)#

Integrating factor

#e^(-(1/2)intdx)=e^(-x/2)#

multiply #(1)# by #e^(-x/2)#

#e^(-x/2)(dy)/(dx)-1/2e^(-x/2)y=1/2#

#=>d/(dx)(ye^(-1/2x))=1/2#

integrating

#ye^(-1/2x)=1/2x+C#

#':.y=1/2xe^(x/2)+Ce^(x/2)#