1
GATE ME 1993
+1
-0.3
The function $$f\left( {x,y} \right) = {x^2}y - 3xy + 2y + x$$ has
A
No local extremum
B
One local maximum but no local minimum
C
One local minimum but no local maximum
D
One local minimum and one local maximum
2
GATE ME 1993
Fill in the Blanks
+1
-0
The differential equation $${y^{11}} + y = 0\,$$ is subjected to the conditions $$y(0) = 0,$$ $$\,\,\,y\left( \lambda \right) = 0.\,\,$$ In order that the equation has non-trivial solutions, the general value of $$\lambda$$ is.
3
GATE ME 1993
+1
-0.3
The differential $$\,\,\,{{{d^2}y} \over {d{x^2}}} + {{dy} \over {dx}} + \sin y = 0\,\,$$ is
A
linear
B
non-linear
C
homogeneous
D
of degree two
4
GATE ME 1993
Fill in the Blanks
+1
-0
Given the differential equation $${y^1} = x - y$$ with initial condition $$y(0)=0.$$ The value of $$y(0.1)$$ calculated numerically upto the third place of decimal by the $${2^{nd}}$$ order Runge-Kutta method with step size $$h=0.1$$ is
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