1
GATE CE 2025 Set 2
Numerical
+1
-0

The "order" of the following ordinary differential equation is $\qquad$ .

$$ \frac{d^3 y}{d x^3}+\left(\frac{d^2 y}{d x^2}\right)^6+\left(\frac{d y}{d x}\right)^4+y=0 $$

Your input ____
2
GATE CE 2025 Set 1
MCQ (Single Correct Answer)
+1
-0.33
Which of the following equations belong/belongs to the class of second-order, linear, homogeneous partial differential equations:
A
$\frac{\partial^2 u}{\partial t^2}=c^2\left(\frac{\partial^2 u}{\partial x^2}+\frac{\partial^2 u}{\partial y^2}\right)+x y$
B
$\frac{\partial^2 u}{\partial x^2}+\frac{\partial^2 u}{\partial y^2}+\frac{\partial^2 u}{\partial z^2}=0$
C
$\frac{\partial u}{\partial t}=c \frac{\partial u}{\partial x}$
D
$\left(\frac{\partial^2 u}{\partial t^2}\right)^2=c^2 \frac{\partial^2 u}{\partial x^2}$
3
GATE CE 2024 Set 2
MCQ (Single Correct Answer)
+1
-0.33

A partial differential equation

$$\frac{\partial^2 T}{\partial x^2} + \frac{\partial^2 T}{\partial y^2} = 0$$

is defined for the two-dimensional field $T: T(x, y)$, inside a planar square domain of size 2 m × 2 m. Three boundary edges of the square domain are maintained at value $T = 50$, whereas the fourth boundary edge is maintained at $T = 100$.

The value of $T$ at the center of the domain is

A

50.0

B

62.5

C

75.0

D

87.5

4
GATE CE 2024 Set 2
MCQ (Single Correct Answer)
+1
-0.33

Consider two Ordinary Differential Equations (ODEs):

P: $ \dfrac{dy}{dx} = \dfrac{x^4 + 3x^2 y^2 + 2y^4}{x^3 y} $

Q: $ \dfrac{dy}{dx} = -\dfrac{y^2}{x^2} $

Which one of the following options is CORRECT?

A

P is a homogeneous ODE and Q is an exact ODE.

B

P is a homogeneous ODE and Q is not an exact ODE.

C

P is a nonhomogeneous ODE and Q is an exact ODE.

D

P is a nonhomogeneous ODE and Q is not an exact ODE.

GATE CE Subjects
EXAM MAP