# Math Help - Solve

1. ## Solve

Solve

x'+y=t
y'-x=-t

I am confused, and need some guidence!

2. Originally Posted by mandy123
Solve

x'+y=t
y'-x=-t

I am confused, and need some guidence!
Differentiate the first again:

$x''+y'=1$

so, substituting the second into the first:

$x''+x=t+1$

and for $y$ you can differentiate the second and substitute the first.

CB

3. ok, but shouldn't it be

x'' + x = 1 + t

and then

y'' + y = t - 1

what happened to the 1 in your first equation?

4. Originally Posted by mandy123
ok, but shouldn't it be

x'' + x = 1 + t Mr F says: Yes. CB made a small mistake (he makes one every year). But it's the method that's important.

and then

y'' + y = t - 1

what happened to the 1 in your first equation?
Your equations are correct and there should be no problem solving them.

5. Originally Posted by mandy123
ok, but shouldn't it be

x'' + x = 1 + t

and then

y'' + y = t - 1

what happened to the 1 in your first equation?
Typo now corrected.

CB

6. so would my answer of

x(t)=Acos(t) + Bsin(t) + 1 + t
y(t)=Acos(t) + Bsin(t) - 1 + t

be the right answer, or did i mess up somehow?

7. Originally Posted by mandy123