1
GATE CE 2023 Set 1
Numerical
+2
-0

The differential equation,

$\rm \frac{du}{dt}+2tu^2=1,$

is solved by employing a backward difference scheme within the finite difference framework. The value of š‘¢ at the (š‘› āˆ’ 1) th time-step, for some š‘›, is 1.75. The corresponding time (t) is 3.14 s. Each time step is 0.01 s long. Then, the value of (un - un -1) _________ is (round off to three decimal places). 

Your input ____
2
GATE CE 2022 Set 1
Numerical
+2
-0

Consider the differential equation

$${{dy} \over {dx}} = 4(x + 2) - y$$

For the initial condition y = 3 at x = 1, the value of y at x = 1.4 obtained using Euler's method with a step-size of 0.2 is ________. (round off to one decimal place)

Your input ____
3
GATE CE 2016 Set 1
MCQ (Single Correct Answer)
+2
-0.6
The solution of the partial differential equation $${{\partial u} \over {\partial t}} = \alpha {{{\partial ^2}u} \over {\partial {x^2}}}$$ is of the form
A
$$C\cos \left( {kt} \right)\left[ {{C_1}{e^{\left( {\sqrt {k/\alpha } } \right)x}} + {C_2}{e^{ - \left( {\sqrt {k/\alpha } } \right)x}}} \right]$$
B
$$C\,{e^{kt}}\left[ {{C_1}{e^{\left( {\sqrt {k/\alpha } } \right)x}} + {C_2}{e^{ - \left( {\sqrt {k/\alpha } } \right)x}}} \right]$$
C
$$C{e^{kt}}\left[ {{C_1}\,\cos \left( {\sqrt {k/\alpha } } \right)x + {C_2}\,\sin \left( { - \sqrt {k/\alpha } } \right)x} \right]$$
D
$$C\sin \left( {kt} \right)\left[ {{C_1}\,\cos \left( {\sqrt {k/\alpha } } \right)x + {C_2}\,\sin \left( { - \sqrt {k/\alpha } } \right)x} \right]$$
4
GATE CE 2015 Set 1
MCQ (Single Correct Answer)
+2
-0.6
Consider the following differential equation
$$x\left( {y\,dx + x\,dy} \right)\cos \left( {{y \over x}} \right)$$
$$\,\,\,\,\,\,\,\,\,\, = y\left( {x\,dy - y\,dx} \right)\sin \left( {{y \over x}} \right)$$

Which of the following is the solution of the above equation ($$C$$ is an arbitrary constant)

A
$${x \over y}\cos {y \over x} = C$$
B
$${x \over y}\sin {y \over x} = C$$
C
$$xy\,\cos {y \over x} = C$$
D
$$xy\,\sin {y \over x} = C$$
GATE CE Subjects
EXAM MAP