Given Equation,
"x'+x-y=e^{2t}"
"\\frac{dx}{dt}+x=y+e^{2t}"
Integrated factor, i.f="e^{\\int 1.dt}"
="e^t"
solution is given by,
"x\\times i.f.=\\int i.f.\\times (y+e^{2t})dt+c"
"xe^t=\\int(y+e^{2t})e^tdt+c"
"xe^t=ye^t+\\frac{e^{3t}}{3}+c"
"x=y+\\frac{e^{2t}}{3}+ce^{-t}"
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