Finding a solution given initial value problem
Code:
y'-y=7te2t , y(0)=1
I would like to know how to solve this Differential Equation. I think I have to find the integrating factor.
It does look like it follows the the standard form So the integrating factor is e∫px
Would the integrating factor be e∫-y ?
Thanks
Re: Finding a solution given initial value problem
Your integrating factor would be:
$\displaystyle \mu(t)=e^{\int(-1)\,dt}=e^{-t}$
Multiplying the ODE by this factor will give you the product of differentiation on the left:
$\displaystyle e^{-t}\frac{dy}{dt}-e^{-t}y=7te^t$
$\displaystyle \frac{d}{dt}\left(e^{-t}y \right)=7te^t$
$\displaystyle \int\,d\left(e^{-t}y \right)=7\int te^t\,dt$
Now, use integration by parts on the right...
Re: Finding a solution given initial value problem
How do you insert mathematical functions on these forums the way you inserted the integral sign?
And thanks for the integrating factor.
Re: Finding a solution given initial value problem
Use the TEX tags, for example enclosing the code \int_a^b f(x)\,dx=F(b)-F(a) within the tags produces:
$\displaystyle \int_a^b f(x)\,dx=F(b)-F(a)$