1
GATE PI 2015
MCQ (Single Correct Answer)
+1
-0.3
The solution to $$\,6y{y^1} - 25x = 0\,\,$$ represents a
A
family of circles
B
family of ellipses
C
family of parabolas
D
family of hyperbolas
2
GATE PI 2015
MCQ (Single Correct Answer)
+1
-0.3
The solution to $$\,\,{x^2}{y^{11}} + x{y^1} - y = 0\,\,$$ is
A
$$y = {C_1}{x^2} + {C_2}{x^{ - 3}}$$
B
$$y = {C_1} + {C_2}{x^{ - 2}}$$
C
$$y = {C_1}x + {{{C_2}} \over x}$$
D
$$y = {C_1}x + {C_2}{x^4}$$
3
GATE PI 2009
MCQ (Single Correct Answer)
+1
-0.3
The homogeneous part of the differential equation $$\,{{{d^2}y} \over {d{x^2}}} + p{{dy} \over {dx}} + qy = r\,\,$$ ( $$p, q, r$$ are constants) has real distinct roots if
A
$${p^2} - 4q > 0$$
B
$${p^2} - 4q < 0$$
C
$${p^2} - 4q = 0$$
D
$${p^2} - 4q = r$$
4
GATE PI 2008
MCQ (Single Correct Answer)
+1
-0.3
The solutions of the differential equation $${{{d^2}y} \over {d{x^2}}} + 2{{dy} \over {dx}} + 2y = 0\,\,$$ are
A
$${e^{ - \left( {1 + i} \right)x}},{e^{ - \left( {1 - i} \right)x}}$$
B
$${e^{\left( {1 + i} \right)x}},\,\,{e^{\left( {1 - i} \right)x}}$$
C
$${e^{ - \left( {1 + i} \right)x}},\,\,{e^{\left( {1 + i} \right)x}}$$
D
$${e^{\left( {1 + i} \right)x}},\,\,{e^{ - \left( {1 + i} \right)x}}$$
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