differential equation w/ initial condition

**thedoge** · February 4th 2007, 07:00 PM

Solve the differential equation with given conditions

(dy/dt)=(1/2)y

y(2)=100

**ThePerfectHacker** · February 4th 2007, 07:08 PM

Originally Posted by thedoge

Solve the differential equation with given conditions

(dy/dt)=(1/2)y

y(2)=100

$y'=\frac{1}{2}y$
Divide by $y$ .
First check if $y=0$ is a solution (it is).
Now look for other solutions $y\not = 0$ ,
$\frac{y'}{y}=\frac{1}{2}$
Integrate,
$\int \frac{y'}{y} dx = \int\frac{1}{2} dx$
Thus,
$\ln |y|=\frac{1}{2}x+C'$
Thus, $e^{\ln |y|}=e^{\frac{1}{2}x+C'}$
$|y|=Ce^{\frac{1}{2}x},C>0$
$y=Ce^{\frac{1}{2}x}$
$100=Ce^{\frac{1}{2}(2)}$
$100=Ce^{1}=Ce$
$C=100/e=100e^{-1}$ .
Thus,
$y=Ce^{\frac{1}{2}x}=100e^{-1}e^{\frac{1}{2}x}=100e^{\frac{1}{2}x-1}$

**thedoge** · February 4th 2007, 07:14 PM

As fast and amazing as usual PH.

If you don't mind me asking, do you have a specific profession outside this forum? You seem to be a master of mathematics which should open up about any occupation to you

**ThePerfectHacker** · February 4th 2007, 07:26 PM

Originally Posted by thedoge

If you don't mind me asking, do you have a specific profession outside this forum?

Yes! I am a fashion designer.

**thedoge** · February 4th 2007, 07:27 PM

Haha. A comedian too.

Unless you're serious. One can never know online;]

**thedoge** · February 4th 2007, 07:59 PM

Hrm. I follow everything you said perfectly and even worked it out that way myself, but apparently this problem needs to evaluate to a number.

What is the value of x?

Nevermind. I see what the problem was.

*** for future reader's reference replace the x in 100*e^(.5x-1) with a t

Thread: differential equation w/ initial condition

LinkBack

Thread Tools

Display

differential equation w/ initial condition

Similar Math Help Forum Discussions

Differential Equation w/ Boundary Condition y(1) = e

Solving differential equations with Initial condition

Differential Equation: Initial Value

diffusion equation with initial condition

Differential equation and initial condition

Search Tags