1
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
$$1$$
2
GATE CE 1999
+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
$$y = {e^x} + c$$
3
GATE CE 1997
+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
$${{{\partial ^2}f} \over {\partial {x^2}}} = {{{\partial ^2}g} \over {\partial {y^2}}}$$
4
GATE CE 1995
+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
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