Question

The particular solution of the differential equation dy /dt = 2y for which y(0) = 60 is

a: y = 60e^2t
b: y = 60 e^0.5t
c: y = 59 + e^t
d: y = 30e^t

Answer 1

Firstly bring \(2y\) on left hand side..

Answer 2

\[\frac{dy}{dt} - 2y = 0\]

Answer 3

ok what happens next? :)

Answer 4

a: y = 60e^2t

Answer 5

It is basically a Linear Equation : It is precisely of the form in general:
\[\frac{dy}{dt} + Py = Q\]
P and Q are any function of \(t\).

Answer 6

@nirmalnema you are going against Code of Conduct of this site..

Answer 7

http://openstudy.com/code-of-conduct

Read this..

Answer 8

For that equation that I have written above :
General Solution is given by :
\[y (I.F) = \int\limits (Q \times I.F ) dt\]

Answer 9

And I.F is given by :
\[\large I.F = e^{\int\limits P. dt}\]

Answer 10

dy/dt=2y
dy/2y=dt
integrating both side..

Answer 11

Yes, for sure, you can use here, Variable Separable Method too..

Answer 12

yup...

Answer 13

you carry on then.. :)

Answer 14

thank u guys!! :)