Thread: calculus help!

please help with these problems, any of them! it would be of great help! thanks!




1. suppose that A is a constant. Verify that x(t)=1+t+Ae^t is a solution of the differential equation x'=x-t


2. Suppose that A and B are constants. Verify that y(x)=A ln(x)+B+x is a solution of the differential equation xy''+y'=1

Originally Posted by cottekr

please help with these problems, any of them! it would be of great help! thanks!




1. suppose that A is a constant. Verify that x(t)=1+t+Ae^t is a solution of the differential equation x'=x-t


2. Suppose that A and B are constants. Verify that y(x)=A ln(x)+B+x is a solution of the differential equation xy''+y'=1

All you need to do is substitute the values given into the DE. I'll help you start the first one:

since , we see that

Substituting this into the DE, we see that

I leave the simplification for you.

This should give you enough help to do the second problem on your own.

--Chris