1
GATE CE 2023 Set 2
MCQ (Single Correct Answer)
+2
-0.67

The solution of the differential equation

$\rm \frac{d^3y}{dx^3}-5.5\frac{d^2y}{dx^2}+9.5\frac{dy}{dx}-5y=0$

is expressed as 𝑦 = 𝐢1𝑒2.5π‘₯ + 𝐢2𝑒𝛼π‘₯ + 𝐢3𝑒𝛽π‘₯ , where 𝐢1, 𝐢2, 𝐢3, 𝛼, and 𝛽 are constants, with Ξ± and Ξ² being distinct and not equal to 2.5. Which of the following options is correct for the values of 𝛼 and 𝛽?

A
1 and 2
B
βˆ’1 and βˆ’2
C
2 and 3
D
βˆ’2 and βˆ’3
2
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 𝑒 at the (𝑛 βˆ’ 1) th time-step, for some 𝑛, 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 ____
3
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 ____
4
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
$$C\sin \left( {kt} \right)\left[ {{C_1}\,\cos \left( {\sqrt {k/\alpha } } \right)x + {C_2}\,\sin \left( { - \sqrt {k/\alpha } } \right)x} \right]$$
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