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# Answer to Question #229238 in Chemical Engineering for Lokika

Question #229238

The yp value of (D²− 3D+ 2)y = e^{3x}, choose the correct answer

A) 1/2 e^{3x}

B) e^{3x}

C) 2e^{3x}. D) 3e^{3x}

1
2021-09-04T01:00:59-0400

"\\left(D^2-3D+2\\right)y=e^{3x}\\\\\n\\mathrm{A\\:linear\\:non-homogeneous\\:ODE\\:with\\:constant\\:coefficients\\:has\\:the\\:form\\:of}\\:\\left(a_nD^n+...+a_1D+a_0\\right)y=g\\left(x\\right)\\\\\n\\mathrm{The\\:general\\:solution\\:to}\\:\\left(a_nD^n+...+a_1D+a_0\\right)y=g\\left(x\\right)\\:\\mathrm{can\\:be\\:written\\:as}\\\\\ny=y_h+y_p\\\\\n_h\\mathrm{\\:is\\:the\\:solution\\:to\\:the\\:homogeneous\\:ODE}\\:\\left(a_nD^n+...+a_1D+a_0\\right)y=0\\\\\ny_p\\mathrm{,\\:the\\:particular\\:solution,\\:is\\:any\\:function\\:that\\:satisfies\\:the\\:non-homogeneous\\:equation}\\\\\ny=c_1e^{2x}+c_2e^x\\\\\n\\mathrm{The\\:general\\:solution\\:}y=y_h+y_p\\mathrm{\\:is:}\\\\\ny=c_1e^{2x}+c_2e^x+\\frac{1}{2}e^{3x}"

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