MTH401 Quiz 2 November 2025

Question:

If y=2+xy=2+xy = 2 + x , then which of the following is true for it?

1. Its annihilator operator is D+1
2. Its annihilator operator is D3D3{D^3}
3. Its annihilator operator is D
4. Its annihilator operator is D2D2{D^2}

Copied: 11/25/2025, 10:40:34 AM

Question:

If y=c1ex+c2e4xy=c1ex+c2e4xy = {c_1}{e^x} + {c_2}{e^{4x}} is the complementary solution of �y 2 2"�5�y 2�+�4�y�=�8�e�x�y 3"�5�y 2�+�4�y�=�8�e�x�y�'�'� �-� �5�y�'� �+� �4�y� �=� �8�{�e�^�x�}� �,� �t�h�e�n� �t�h�e� �g�e�n�e�r�a�l� �f�o�r�m� �o ypyp{y_p}=_________.

A. None of these B. AxexAxexAx{e^x} C. AexAexA{e^x} D. (Ax+B)e4x(Ax+B)e4x(Ax + B){e^{4x}}

Copied: 11/25/2025, 10:40:48 AM

Question:

g(x)=5x+7,thentheassumedparticularsolutionypcouldbe_________.Considerthenon - homogeneouslineardifferential �e�q�u�a�t�i�o�n�,�a�n�y�(�n�)�+�a�n"�1�y�(�n"�1�)�+�.�.�.�+�a�1�y 2�+�a�0�y�=�g�(�x�)�.� �I�f�t�h�e�i�n�p�u�t�f�u�n�c�t�i�o�n�,�g�(�x�)�=�5�x�+�7�,�t�h�e�n�t�h�e�a�s�s�u�m�e�d� ouldbe_________.\begin{gathered}

{\text{Consider}}\,\,{\text{the}}\,\,{\text{non -

homogeneous}}\,\,{\text{linear}}\,\,{\text{differential}}\,\,{\text{equation,}}\,\,{a_n}{y^{(n)}} + {a_{n - 1}}{y^{(n - 1)}} + ... + {a_1}y' + {a_0}y = g(x).\,\, \hfill \\\ If\,\,{\text{the}}\,\,{\text{input}}\,\,{\text{function,}}\,\,g(x) = 5x + 7,\,\,{\text{then}}\,\, {\text{the}}\,\,{\text{assumed}}\,\,{\text{particular}}\,\,{\text{solution}}\,\,{y_p}\,\,{\text{could}}\,\,{\text{be}}\,\,{\text{____

_____}}{\text{.}}\, \hfill \\\\

\end{gathered}

A. AAA B. Ax2+Bx+CAx2+Bx+CA{x^2} + Bx + C C. Ax3+Bx2+Cx+DAx3+Bx2+Cx+DA{x^3} + B{x^2} + Cx + D D. Ax+BAx+BAx + B

Copied: 11/25/2025, 10:41:01 AM

Question:

�g�(�x�)�=�3�x�2"�2�,�t�h�e�n�t�h�e�a�s�s�u�m�e�d�p�a�r�t�i�c�u�l�a�r�s�o�l�u�t�i�o�n�y�p�c�o�u�l�d�b�e�_�_�_�_�_�_�_�_�_�.�C�o�n�s�i�d�e�r�t�h�e �e�q�u�a�t�i�o�n�,�a�n�y�(�n�)�+�a�n"�1�y�(�n"�1�)�+�.�.�.�+�a�1�y 2�+�a�0�y�=�g�(�x�)�.� �I�f�t�h�e�i�n�p�u�t�f�u�n�c�t�i�o�n�,�g�(�x�)�=�3�x�2"�2� couldbe_________.\begin{gathered} {\text{Consider}}\,\,{\text{the}}\,\,{\text{non - homogeneous}}\,\,{\text{linear}}\,\,{\text{differential}}\,\,{\text{equation,}}\,\,{a_n}{y^{(n)}} + {a_{n - 1}}{y^{(n - 1)}} + ... + {a_1}y' + {a_0}y = g(x).\,\, \hfill \\\ If\,\,{\text{the}}\,\,{\text{input}}\,\,{\text{function,}}\,\,g(x) = 3{x^2} - 2,\,\,{\text{then} }\,\,{\text{the}}\,\,{\text{assumed}}\,\,{\text{particular}}\,\,{\text{solution}}\,\,{y_p}\,\,{\text{could}}\,\,{\text{be}}\,\,{\text{__ _______}}{\text{.}}\, \hfill \\\\ \end{gathered}

A. AAA B. Ax2+Bx+CAx2+Bx+CA{x^2} + Bx + C C. Ax+BAx+BAx + B D. Ax3+Bx2+Cx+DAx3+Bx2+Cx+DA{x^3} + B{x^2} + Cx + D

Copied: 11/25/2025, 10:41:32 AM

Question:

In the population growth model, the solution of the differential equation is given by ______.

A. A(t)=A0/2A(t)=A0/2A(t) = {A_0}/2 B. A(t)=A0ektA(t)=A0ektA(t) = {A_0}{e^{kt}} C. A(t)=kektA(t)=kektA(t) = k{e^{kt}} D. A(t)=A0/2A(t)=A0/2A(t) = {A_0}/2

Copied: 11/25/2025, 10:41:49 AM

Question:

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