1
GATE IN 2006
MCQ (Single Correct Answer)
+2
-0.6
For initial value problem $$\,\mathop y\limits^{ \bullet \bullet } + 2\,\mathop y\limits^ \bullet + \left( {101} \right)y = \left( {10.4} \right){e^x},y\left( 0 \right) = 1.1\,\,$$ and $$y(0)=-0.9.$$ Various solutions are written in the following groups. Match the type of solution with the correct expression.

Group-$${\rm I}$$
$$P.$$$$\,\,\,\,$$ General solution of Homogeneous equations
$$Q.$$$$\,\,\,\,$$ Particular integral
$$R.$$$$\,\,\,\,$$ Total solution satisfying boundary Conditions

Group-$${\rm II}$$
$$(1)$$$$\,\,\,\,$$ $$0.1\,{e^x}$$
$$(2)$$$$\,\,\,\,$$ $$\,{e^{ - x}}\left[ {A\,\cos \,10x + B\,\sin \,10x} \right]$$
$$(3)$$$$\,\,\,\,$$ $${e^{ - x}}\,\cos \,10x + 0.1\,{e^x}$$

A
$$P - 2,\,\,Q - 1,\,\,R - 3$$
B
$$P - 1,\,\,Q - 3,\,\,R - 2$$
C
$$P - 1,\,\,Q - 2,\,\,R - 3$$
D
$$P - 3,\,\,Q - 2,\,\,R - 1$$
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