1
GATE CE 2014 Set 2
MCQ (Single Correct Answer)
+1
-0.3
The integrating factor for the differential equation $${{dP} \over {dt}} + {k_2}\,P = {k_1}{L_0}{e^{ - {k_1}t}}\,\,$$ is
A
$${e^{ - {k_1}t}}\,$$
B
$${e^{ - {k_2}t}}\,$$
C
$${e^{ {k_1}t}}\,$$
D
$${e^{ {k_2}t}}\,$$
2
GATE CE 2011
MCQ (Single Correct Answer)
+1
-0.3
The solution of the differential equation $${{dy} \over {dx}} + {y \over x} = x$$ with the condition that $$y=1$$ at $$x=1$$ is
A
$$y = {2 \over {3{x^2}}} + {x \over 3}$$
B
$$y = {x \over 2} + {1 \over {2x}}$$
C
$$y = {2 \over 3} + {x \over 3}$$
D
$$y = {2 \over {3x}} + {{{x^2}} \over 3}$$
3
GATE CE 2010
MCQ (Single Correct Answer)
+1
-0.3
The order and degree of a differential equation $${{{d^3}y} \over {d{x^3}}} + 4\sqrt {{{\left( {{{dy} \over {dx}}} \right)}^3} + {y^2}} = 0$$ are respectively
A
$$3$$ and $$2$$
B
$$2$$ and $$3$$
C
$$3$$ and $$3$$
D
$$3$$ and $$1$$
4
GATE CE 2010
MCQ (Single Correct Answer)
+1
-0.3
The partial differential equation that can be formed from $$z=ax+by+ab$$ has the form $$\,\,\left( {p = {{\partial z} \over {\partial x}},q = {{\partial z} \over {\partial y}}} \right)\,\,$$
A
$$z=px+qy$$
B
$$z=px-qy$$
C
$$z=px+qy+pq$$
D
$$z=qy+pq$$
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Fluid Mechanics and Hydraulic Machines
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