1
GATE ME 2014 Set 4
+1
-0.3
The solution of the initial value problem $$\,\,{{dy} \over {dx}} = - 2xy;y\left( 0 \right) = 2\,\,\,$$ is
A
$$1 + {e^{ - {x^2}}}$$
B
$$2{e^{ - {x^2}}}$$
C
$$1 + {e^{ {x^2}}}$$
D
$$2{e^{ {x^2}}}$$
2
GATE ME 2013
+1
-0.3
The partial differential equation $$\,\,{{\partial u} \over {\partial t}} + u{{\partial u} \over {\partial x}} = {{{\partial ^2}u} \over {\partial {x^2}}}\,\,\,$$ is a
A
Linear equation of order $$2$$
B
Non-linear equation of order $$1$$
C
Linear equation of order $$1$$
D
non-linear equation of order $$2$$
3
GATE ME 2011
+1
-0.3
Consider the differential equation $${{dy} \over {dx}} = \left( {1 + {y^2}} \right)x\,\,.$$ The general solution with constant $$'C'$$ is
A
$$y = \tan \left( {{{{x^2}} \over 2}} \right) + C$$
B
$$y = {\tan ^2}\left( {{x \over 2} + C} \right)$$
C
$$y = {\tan ^2}\left( {{x \over 2}} \right) + C$$
D
$$y = \tan \left( {{{{x^2}} \over 2} + C} \right)$$
4
GATE ME 2010
+1
-0.3
The blasius equation $$\,{{{d^3}f} \over {d{\eta ^3}}} + {f \over 2}\,{{{d^2}f} \over {d{\eta ^2}}} = 0\,\,\,\,$$ is a
A
2nd order non-linear ordinary differential equation
B
3rd order non-linear ordinary differential equation
C
3rd order linear ordinary differential equation
D
mixed order non-linear ordinary differential equation
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