# calculus help!

• Oct 28th 2008, 06:27 PM
cottekr
calculus help!

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
• Oct 29th 2008, 07:30 AM
Chris L T521
Quote:

Originally Posted by cottekr

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