1
GATE ME 2017 Set 1
+1
-0.3
Consider the following partial differential equation for $$u(x,y)$$ with the constant $$c>1:$$ $$\,{{\partial u} \over {\partial y}} + c{{\partial u} \over {dx}} = 0\,\,$$ solution of this equation is
A
$$u(x,y)=f(x+cy)$$
B
$$u(x,y)=f(x-cy)$$
C
$$u(x,y)=f(cx+y)$$
D
$$u(x,y)=f(cx-y)$$
2
GATE ME 2015 Set 2
+1
-0.3
Consider the following differential equation $${{dy} \over {dt}} = - 5y;$$ initial condition: $$y=2$$ at $$t=0.$$
The value of $$y$$ at $$t=3$$ is
A
$$- 5{e^{ - 10}}$$
B
$$2{e^{ - 10}}$$
C
$$2{e^{ - 15}}$$
D
$$- 15{e^2}$$
3
GATE ME 2015 Set 1
+1
-0.3
Find the solution of $${{{d^2}y} \over {d{x^2}}} = y$$ which passes through origin and the point $$\left( {ln2,{3 \over 4}} \right)$$
A
$$y = {1 \over 2}{e^x} - {e^{ - x}}$$
B
$${1 \over 2}\left( {{e^x} + {e^{ - x}}} \right)$$
C
$$y = {1 \over 2}\left( {{e^x} - {e^{ - x}}} \right)$$
D
$${1 \over 2}{e^x} + {e^{ - x}}$$
4
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
$$2{e^{ {x^2}}}$$
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