1994-1-c-math
Integrating factor for the differential equation \(\dfrac {dy}{dx} + P(x) y = Q(x)\) is
1994-1-e-math
The solution for the differential equation \(\dfrac {d^2y}{dx^2} + 5\dfrac {dy}{dx} + 6y = 0\) is
2000-1-3-math
The integrating factor for the differential equation: \((\cos ^2x)\dfrac {dy}{dx} + y = \tan x\), is
2004-4-math
The differential equation \(\displaystyle \frac {d^2y}{dx^2} + \sin x \frac {dy}{dx} + ye^x = \sinh x \) is
2005-1-math
Match the following, where \(x\) is the spatial coordinate and \(t\) is time.
| Group I | Group II |
|---|---|
| P) Wave equation | I) \(\displaystyle \frac {\partial c}{\partial t} = \alpha \frac {\partial c}{\partial x}\) |
| Q) Heat equation | II) \(\displaystyle \frac {\partial c}{\partial t} = \alpha ^2 \frac {\partial ^2 c}{\partial x^2}\) |
| III) \(\displaystyle \frac {\partial ^2 c}{\partial t^2} = \alpha ^2 \frac {\partial c}{\partial x}\) | |
| IV) \(\displaystyle \frac {\partial ^2 c}{\partial t^2} = \alpha ^2 \frac {\partial ^2 c}{\partial x^2}\) |
2008-2-math
Which ONE of the following is NOT a solution of the differential equation \(\displaystyle \frac {d^2y}{dx^2} + y = 1\)? ___________
2012-2-math
If \(a\) and \(b\) are arbitrary constants, then the solution to the differential equation \(\displaystyle \frac {d^2y}{dx^2} - 4y = 0 \) is
1995-3-a-math
Match the items in the left column with the appropriate items in the right column.
I. \(y=x^2\)
II. \(dy/dx=2x\)
1998-2-2-math
The differential equation \(\dfrac {d^2x}{dt^2} + 3\dfrac {dx}{dt} + 2x = 0\) will have a solution of the form
2000-2-4-math
The general solution of \(\dfrac {d^4y}{dx^4} + 2\dfrac {d^2y}{dx^2} + y = 0\) is ___________ (where \(C_1, C_2, C_3\), and \(C_4\) are constants).
2003-32-math
The value of \(y\) as \(t \rightarrow \infty \) for the following differential equation for an initial value of \(y(1) = 0\) is \[ (4t^2+1)\frac {dy}{dt} + 8yt - t = 0 \]
2003-36-math
The differential equation \(\displaystyle \frac {d^2x}{dt^2} + 10\frac {dx}{dt} + 25x = 0 \) will have a solution of the form ___________ (where \(C_1\) and \(C_2\) are constants).
2004-35-math
The differential equation for the variation of the amount of salt \(x\) in a tank with time \(t\) is given by \(\displaystyle \frac {dx}{dt} + \frac {x}{20} = 10\). \(x\) is in kg and \(t\) is in minutes. Assuming that there is no salt in the tank initially, the time (in min) at which the amount of salt increases to 100 kg is
2005-36-math
What condition is to be satisfied so that the solution of the differential equation \[ \frac {d^2y}{dx^2} + a\frac {dy}{dx} + by = 0\] is of the form \(y=(C_1+C_2x)e^{mx}\), where \(C_1\) and \(C_2\) are constants of integration?
2008-21-math
Which ONE of the following transformations \(\{u=f(y)\}\) reduces \[ \frac {dy}{dx} + Ay^3+By=0 \] to a linear differential equation? (\(A\) and \(B\) are positive constants)
2009-22-math
The general solution of the differential equation \[ \frac {d^2y}{dx^2} - \frac {dy}{dx} - 6y = 0 \] with \(C_1\) and \(C_2\) as constants of integration, is
2010-26-math
The solution of the differential equation \[ \frac {d^2y}{dt^2} + 2\frac {dy}{dt} + 2y = 0 \] with the initial conditions \(\displaystyle y(0)=0, \ \left .\frac {dy}{dt}\right |_{t=0} = -1\), is
2011-27-math
Which one of the following choices is a solution of the differential equation given below? \[ \frac {dy}{dx} = \frac {y^2}{x} + \frac {y}{x} - \frac {2}{x} \] Note: \(c\) is a real constant.
2013-27-math
The solution of the differential equation \(\ \displaystyle \frac {dy}{dx}-y^2=0, \ \) given \(y=1\) at \(x=0\) is
2013-28-math
The solution of the differential equation \(\ \displaystyle \frac {d^2y}{dx^2} - \frac {dy}{dx} + 0.25y =0\), given \(y=0\) at \(x=0\) and \(\displaystyle \ \frac {dy}{dx}=1\) at \(x=0\) is
2014-27-math
The integrating factor for the differential equation \(\ \displaystyle \frac {dy}{dx}-\frac {y}{1+x}=(1+x)\ \) is
2014-28-math
The differential equation \(\ \displaystyle \frac {d^2y}{dx^2}+x^2\frac {dy}{dx}+x^3y=e^x \ \) is a
2016-27-math
What is the solution for the second order differential equation \(\displaystyle \frac {d^2y}{dx^2}+y=0\), with the initial conditions \(y|_{x=0}=5\) and \(\displaystyle \left .\frac {dy}{dx}\right |_{x=0}=10\) ?
EC-2017-S1-29-math
Which one of the following is the general solution of the first order differential equation \[\frac {dy}{dx} = (x+y-1)^2\] where \(x, y\) are real?
1994-2-c-math
\(M dx + N dy\) is an exact differential when ---------
1994-2-g-math
The differential equation \(\dfrac {d^2y}{dx^2} + y = 0\), with the conditions \(y(0)=0\) and \(y(1)=1\) is called a --------- value problem.
1995-3-b-math
Match the items in the left column with the appropriate items in the right column.
| (I) \(dy/dx + 5y=0, \, y(0) = y_0\) | (A) \(y=y_0+5x\) |
| (II) \(dy/dx + 5=0, \, y(0) = y_0\) | (B) \(y=y_0-5x\) |
| (C) \(y=y_0e^{-5x}\) | |
| (D) \(y=y_0e^{5x}\) |
1996-10-math
Solve \[ \dfrac {dy}{dx} + 0.6 y = 6e^{-0.5x} \] using the integrating factor method, given \(y=1\) at \(x=0\).
1999-4-math
Solve \(\dfrac {dy}{dx} - 6xy = -6x\) by the following methods:
Last Modified on: 03-May-2024
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