GATE ME 2025 | Differential Equations Question 1 | Engineering Mathematics

GATE ME 2025

MCQ (Single Correct Answer)

-0.33

For the differential equation given below, which one of the following options is correct?

$$ \frac{\partial^2 u}{\partial x^2}+\frac{\partial^2 u}{\partial y^2}=0,0 \leq x \leq 1,0 \leq y \leq 1 $$

$u=e^{x+y}$ is a solution for all $x$ and $y$

$u=e^x \sin y$ is a solution for all $x$ and $y$

$u=\sin x \sin y$ is a solution for all $x$ and $y$

$u=\cos x \cos y$ is a solution for all $x$ and $y$

GATE ME 2022 Set 1

MCQ (Single Correct Answer)

-0.33

Solution of ∇²T = 0 in a square domain (0 < x < 1 and 0 < y < 1) with boundary conditions:

T(x, 0) = x; T(0, y) = y; T(x, 1) = 1 + x; T(1, y) = 1 + y is

T(x, y) = x - xy + y

T(x, y) = x + y

T(x, y) = -x + y

T(x, y) = x + xy + y

GATE ME 2017 Set 1

MCQ (Single Correct Answer)

-0.3

The differential equation $$\,{{{d^2}y} \over {d{x^2}}} + 16y = 0$$ for $$y(x)$$ with the two boundary conditions $${\left. {{{dy} \over {dx}}} \right|_{x = 0}} = 1$$ and $${\left. {{{dy} \over {dx}}} \right|_{x = {\pi \over 2}}} = - 1$$ has

no solution

exactly two solutions

exactly one solution

infinitely many solutions

GATE ME 2017 Set 1

MCQ (Single Correct Answer)

-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

$$u(x,y)=f(x+cy)$$

$$u(x,y)=f(x-cy)$$

$$u(x,y)=f(cx+y)$$

$$u(x,y)=f(cx-y)$$