1
GATE CE 2007
+1
-0.3
The degree of the differential equation $$\,{{{d^2}x} \over {d{t^2}}} + 2{x^3} = 0\,\,$$ is
A
$$0$$
B
$$1$$
C
$$2$$
D
$$3$$
2
GATE CE 2007
+1
-0.3
A body originally at $${60^ \circ }$$ cools down to $$40$$ in $$15$$ minutes when kept in air at a temperature of $${25^ \circ }$$c. What will be the temperature of the body at the and of $$30$$ minutes?
A
$${35.2^ \circ }C$$
B
$${31.5^ \circ }C$$
C
$${28.7^ \circ }C$$
D
$${15^ \circ }C$$
3
GATE CE 2006
+1
-0.3
The solution of the differential equation $$\,{x^2}{{dy} \over {dx}} + 2xy - x + 1 = 0\,\,\,$$ given that at $$x=1,$$ $$y=0$$ is
A
$$\,{1 \over 2} - {1 \over x} + {1 \over {2{x^2}}}$$
B
$$\,{1 \over 2} - {1 \over x} - {1 \over {2{x^2}}}$$
C
$${1 \over 2} + {1 \over x} + {1 \over {2{x^2}}}$$
D
$$- {1 \over 2} + {1 \over x} + {1 \over {2{x^2}}}$$
4
GATE CE 2001
+1
-0.3
The number of boundary conditions required to solve the differential equation $$\,\,{{{\partial ^2}\phi } \over {\partial {x^2}}} + {{{\partial ^2}\phi } \over {\partial {y^2}}} = 0\,\,$$ is
A
$$2$$
B
$$0$$
C
$$4$$
D
$$1$$
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