# Thread: calculus help!

1. ## 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

2. 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 $\displaystyle x(t)$ values given into the DE. I'll help you start the first one:

since $\displaystyle x(t)=1+t+Ae^t$, we see that $\displaystyle x'(t)=1+Ae^t$

Substituting this into the DE, we see that $\displaystyle (1+Ae^t)=(1+t+Ae^t)-t$

I leave the simplification for you.

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

--Chris