What command would I use to ask maple to solve the following

$\displaystyle x''=\frac{t+1}{t}x'-\frac{1}{t}x$

with $\displaystyle x_1(t)=e^t$

I know about the dsolve command but I'm not sure how to tell it what the other solution is.

- May 27th 2011, 03:54 PMCarbonUsing maple to solve a an equation where one solution is known
What command would I use to ask maple to solve the following

$\displaystyle x''=\frac{t+1}{t}x'-\frac{1}{t}x$

with $\displaystyle x_1(t)=e^t$

I know about the dsolve command but I'm not sure how to tell it what the other solution is. - May 27th 2011, 04:20 PMTheEmptySet
Here is a screenshot of the maple commands.

Attachment 21608

Now use set

$\displaystyle c_1=0\quad c_2=1$

this gives

$\displaystyle u(t)=(t+1)e^{-t}$

$\displaystyle y=u(t)e^{t}=(t+1)e^{-t}e^{t}=t+1$

So this is the other linearly independent solution.