1
GATE CE 2006
MCQ (Single Correct Answer)
+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
$$ - {1 \over 2} + {1 \over x} + {1 \over {2{x^2}}}$$
2
GATE CE 2001
MCQ (Single Correct Answer)
+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
$$1$$
3
GATE CE 1999
MCQ (Single Correct Answer)
+1
-0.3
If $$c$$ is a constant, then the solution of $${{dy} \over {dx}} = 1 + {y^2}$$ is
A
$$y=sin(x+c)$$
B
$$y=cos(x+c)$$
C
$$y=tan(x+c)$$
D
$$y = {e^x} + c$$
4
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
$${{{\partial ^2}f} \over {\partial {x^2}}} = {{{\partial ^2}g} \over {\partial {y^2}}}$$
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