How do I solve the equation $\frac{d y}{d t} = 2 y - 10$ $dy/dt = 2y - 10$ ?

Question

How do I solve the equation $\frac{d y}{d t} = 2 y - 10$ $dy/dt = 2y - 10$ ?

1 Answer

Impact of this question

30412 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-01-31T20:07:21

You can use a technique known as Separation of Variables.
Take all the $y$ $y$ to one side and the $t$ $t$ on the other...
You get:

$\frac{d y}{2 y - 10} = d t$ $dy/(2y-10)=dt$

Now you can integrate both sides with respect to the correspondent variables:

$\int \frac{1}{2 y - 10} d y = \int d t$ $int1/(2y-10)dy=intdt$
$\int \frac{1}{2 (y - 5)} d y = \int d t$ $int1/(2(y-5))dy=intdt$

And finally
$\frac{1}{2} ln (y - 5) = t + c$ $1/2ln(y-5)=t+c$

Now you can express $y$ $y$ as:
$ln (y - 5) = 2 t + c$ $ln(y-5)=2t+c$
$y - 5 = c_{1} e^{2 t}$ $y-5=c_1e^(2t)$ where $c_{1} = e^{c}$ $c_1=e^c$
$y = c_{1} e^{2 t} + 5$ $y=c_1e^(2t)+5$

You can substitute back to check your result (calculating $\frac{d y}{d t}$ $dy/dt$ ) remembering that now it is: $y = c_{1} e^{2 t} + 5$ $y=c_1e^(2t)+5$

Science

Math

Humanities

... and beyond

How do I solve the equation $\frac{d y}{d t} = 2 y - 10$ $dy/dt = 2y - 10$ ?

1 Answer

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How do I solve the equation dy/dt = 2y - 10dydt=2y−10dy/dt = 2y - 10?

1 Answer

Related questions

Impact of this question

How do I solve the equation $\frac{d y}{d t} = 2 y - 10$ $dy/dt = 2y - 10$ ?