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# Answer to Question #223892 in Chemical Engineering for Lokika

Question #223892

Solve y" + 3y' +2y =1, y(0)=0,y'(0) = 1

1
2021-09-03T07:20:42-0400

"\\mathrm{A\\:second\\:order\\:linear,\\:non-homogeneous\\:ODE\\:has\\:the\\:form\\:of\\:}\\:\\:ay''+by'+cy=g\\left(x\\right)\\\\\n\\mathrm{The\\:general\\:solution\\:to\\:}a\\left(x\\right)y''+b\\left(x\\right)y'+c\\left(x\\right)y=g\\left(x\\right)\\mathrm{\\:can\\:be\\:written\\:as}\\\\\ny=y_h+y_p\\\\\ny_h\\mathrm{\\:is\\:the\\:solution\\:to\\:the\\:homogeneous\\:ODE\\:}a\\left(x\\right)y''+b\\left(x\\right)y'+c\\left(x\\right)y=0\\\\\ny_p\\mathrm{,\\:the\\:particular\\:solution,\\:is\\:any\\:function\\:that\\:satisfies\\:the\\:non-homogeneous\\:equation}\\\\\ny=c_1e^{-t}+c_2e^{-2t}\\\\\n\\mathrm{The\\:general\\:solution\\:}y=y_h+y_p\\mathrm{\\:is:}\\\\\ny=\\frac{1}{2}-\\frac{1}{2}e^{-2t}"

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