Let y=y(t) be a solution of the differen...

Let `y=y(t)` be a solution of the differential equation `(dy)/(dt)+alpha y=gamma e^(-beta t)` where, `alpha>0,beta>0` and `gamma>0`.Then `lim_(t rarr oo)y(t)` is

is `-1`

is `0`

is `1`

does not exist

Text Solution

Verified by Experts

The correct Answer is:

Topper's Solved these Questions

JEE MAINS 2022
JEE MAINS PREVIOUS YEAR|Exercise MATHEMATICS (SECTION - B)|10 Videos
LIMITS AND DERIVATIVES
JEE MAINS PREVIOUS YEAR|Exercise All Questions|14 Videos

Similar Questions

Explore conceptually related problems

Let y=y(t) be a solution to the differential equation y'+2ty=t^(2), then 16(lim)_(tvec oo)(y)/(t)

If y(t) satisfies the differential equation y'(t)+2y(t)=2e^(-2t),y(0)=2 then y(1) equals

Let x=x(t) and y=y(t) be solutions of the differential equations (dx)/(dt)+ax=0 and (dy)/(dt)+by=0] , respectively, a,b in R .Given that x(0)=2,y(0)=1 and 3y(1)=2x(1) ,the value of "t" ,for which, [x(t)=y(t) ,is :

If the solution of the differential equation (2x+3y-2)dx+(4x+6y-7)dy=0,y(0)=3 ,is alpha x beta y+3log_(e) abs(2x+3y-gamma)=6 ,then alpha+2 beta+3 gamma is equal to

Let y=y(x) be solution of the following differential equation e^(y)(dy)/(dx)-2e^(y)sinx+sinxcos^(2)=0,y((pi)/(2))=0 If y(0)=log_(e)(alpha+betae^(-2)) , then 4(alpha+beta) is equal to _____.

If y(t) is a solution of (1+t)(dy)/(dt)-ty=1 and y(0)=-1 then y(1) is

Let x-y sin alpha-z sin beta=0,x sin alpha=z sin gamma-y=0 and x sin beta+y sin gamma-z=0 be the equations of the planes such that alpha+beta+gamma=pi/2(wherealpha,beta and gamma!=0). Then show there is a common line of intersection of the three given planes.

Show that the solution of the equation [(x, y),(z, t)]^(2)=O is [(x,y),(z,t)]=[(pm sqrt(alpha beta),-beta),(alpha,pm sqrt(alpha beta))] where alpha, beta are arbitrary.

If y(t) is a solution of (1+t)(dy)/(dt)-ty+1=0 and y(0)=1 , then : y(1)=…

JEE MAINS PREVIOUS YEAR-JEE MAINS 2023 JAN ACTUAL PAPER-Question

Let the function f(x)=2x^(3)+(2p-7)x^(2)+3(2p-9)x-6 have a maxima for ...
Text Solution
|
Let vec a=-hat i-hat j+hat k,vec a*vec b=1 and vec a timesvec b=hat i-...
Text Solution
|
Let y=y(t) be a solution of the differential equation (dy)/(dt)+alpha ...
Text Solution
|
Let N be the sum of the numbers appeared when two fair dice are rolled...
Text Solution
|
A triangle is formed by X -axis, Y -axis and the line 3x+4y=60.Then th...
Text Solution
|
If int((1)/(3))^(3)|log(e)x|dx=(m)/(n)log(e)(n^2/e), where m and n are...
Text Solution
|
Suppose Anil's mother wants to gave 5 whole fruits to Anil from a bask...
Text Solution
|
Point P(-3,2),Q(9,10) and R(alpha,4) lie on a circle C with PR as its ...
Text Solution
|
If m and n respectively are the numbers of positive and negative value...
Text Solution
|
The remainder when (2023)^(2023) is divided by 35 is
Text Solution
|
25% of the population are smokers.A smoker has 27 times more chances t...
Text Solution
|
If the shortest distance between the line joining the points (1,2,3) a...
Text Solution
|
Let alpha in R and let alpha,beta be the roots of the equation x^(2)+6...
Text Solution
|
For the two positive numbers a,b,if a,b and (1)/(18) are in a geometri...
Text Solution
|
If the coefficient of x^(15) in expansion of (ax^(3)+(1)/(bx^(1/3)))^(...
Text Solution
|
Let the solution curve y=y(x) of the differential equation (dy)/(dx)-(...
Text Solution
|
The number of points on the curve y=54x^(5)-135x^(4)-70x^(3)+180x^(2)+...
Text Solution
|
If tan15^(@)+(1)/(tan75^(@))+(1)/(tan105^(@))+tan195^(@)=2a,then the v...
Text Solution
|
If [t] denotes the greatest integer let,then the value of (3(e-1))/(e)...
Text Solution
|
Let y=x+2,4y=3x+6 and 3y=4x+1 be three tangent lines to the circle (x-...
Text Solution
|