1
GATE CE 1997
MCQ (Single Correct Answer)
+1
-0.3
For the differential equation $$f\left( {x,y} \right){{dy} \over {dx}} + g\left( {x,y} \right) = 0\,\,$$ to be exact is
A
$$\,{{\partial f} \over {\partial y}} = {{\partial g} \over {\partial x}}$$
B
$${{\partial f} \over {\partial x}} = {{\partial g} \over {\partial y}}$$
C
$$f=g$$
D
$${{{\partial ^2}f} \over {\partial {x^2}}} = {{{\partial ^2}g} \over {\partial {y^2}}}$$
2
GATE CE 1995
MCQ (Single Correct Answer)
+1
-0.3
The differential equation $${y^{11}} + {\left( {{x^3}\,\sin x} \right)^5}{y^1} + y = \cos {x^3}\,\,\,\,$$ is
A
homogeneous
B
non-linear
C
$$2$$nd order linear
D
non-homogeneous with constant coefficients
3
GATE CE 1994
MCQ (Single Correct Answer)
+1
-0.3
The necessary & sufficient condition for the differential equation of the form $$\,\,M\left( {x,y} \right)dx + N\left( {x,y} \right)dy = 0\,\,$$ to be exact is
A
$$M=N$$
B
$${{\partial M} \over {\partial x}} = {{\partial N} \over {\partial y}}$$
C
$${{\partial M} \over {\partial y}} = {{\partial N} \over {\partial x}}$$
D
$${{{\partial ^2}M} \over {\partial {x^2}}} = {{{\partial ^2}N} \over {\partial {y^2}}}$$
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Fluid Mechanics and Hydraulic Machines
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