Register

GATE Mechanical 2014 Set 3 | Question: 27

• recategorized by
0 votes
0 votes

Consider two solutions $x(t)=x_1(t)$ and $x(t)=x_2(t)$ of the differential equation $\dfrac{d^2x(t)}{dt^2}+x(t)=0, \: t>0$ such that $x_1(0)=1, \dfrac{dx_1(t)}{dt} \bigg \vert_{t=0}=0$, $x_2(0)=0, \dfrac{dx_2(t)}{dt}\bigg \vert _{t=0}=1$.

The Wronskian $W(t)=\begin{bmatrix} x_1(t) & x_2(t)\\  \\ \dfrac{dx_1(t)}{dt} & \dfrac{dx_2(t)}{dt} \end{bmatrix}$ at $t=\pi /2$ is

  1. $1$
  2. $-1$
  3. $0$
  4. $\pi /2$
• recategorized by
User Avatar

Please log in or register to answer this question.

← PreviousNext →
← Previous in categoryNext in category →
Answer:

Related questions

0 answers
0 votes
Arjun asked Feb 19, 2017
GATE Mechanical 2014 Set 4 | Question: 3
The solution of the initial value problem $\dfrac{dy}{dx}=-2xy$ ; $y(0)=2$ is $1+e^{{-x}^2}$ $2e^{{-x}^2}$ $1+e^{{x}^2}$ $2e^{{x}^2}$
The solution of the initial value problem $\dfrac{dy}{dx}=-2xy$ ; $y(0)=2$ is$1+e^{{-x}^2}$$2e^{{-x}^2}$$1+e^{{x}^2}$$2e^{{x}^2}$
0 answers
0 votes
Arjun asked Feb 26, 2017
GATE2017 ME-2: 27
Consider the differential equation $3y" (x)+27 y (x)=0$ with initial conditions $y(0)=0$ and $y'(0)=2000$. The value of $y$ at $x=1$ is ________.
Consider the differential equation $3y" (x)+27 y (x)=0$ with initial conditions $y(0)=0$ and $y'(0)=2000$. The value of $y$ at $x=1$ is ________.
0 answers
0 votes
gatecse asked Feb 22, 2021
GATE Mechanical 2021 Set 1 | Question: 3
The Dirac-delta function $\left ( \delta \left ( t-t_{0} \right ) \right )$ for $\text{t}$, $t_{0} \in \mathbb{R}$ ... $0$ $\infty$ $e^{sa}$ $e^{-sa}$
The Dirac-delta function $\left ( \delta \left ( t-t_{0} \right ) \right )$ for $\text{t}$, $t_{0} \in \mathbb{R}$, has the following property$$\int_{a}^{b}\varphi \left ...
Voting & Accepting an answer helps improve the community
Link Copied!