# Thread: Is this Diff EQ solution wrong?

1. ## Is this Diff EQ solution wrong?

Hi all,

Here's the problem:

t(dx/dt) + x = t^3

1. dx/dt + x/t = t^2

2. use (1/t) as an integrating factor: e^(int(1/t)dt) = e^(ln t) = t

3. d/dt (xt) = t^3

4. xt = (1/4)t^4 + C

5. x = (1/4)t^3 + C/t

My friend got the answer k(t)(1/t) = t^3/4 + C/t

Did I make a mistake or did he? Or both? Thanks,

Kim

2. Originally Posted by Kim Nu
Hi all,

Here's the problem:

t(dx/dt) + x = t^3

1. dx/dt + x/t = t^2

2. use (1/t) as an integrating factor: e^(int(1/t)dt) = e^(ln t) = t

3. d/dt (xt) = t^3

4. xt = (1/4)t^4 + C

5. x = (1/4)t^3 + C/t

My friend got the answer k(t)(1/t) = t^3/4 + C/t

Did I make a mistake or did he? Or both? Thanks,

Kim
You are correct. How did your friend get $k(t)\cdot{\color{red}\frac{1}{t}}=\frac{t^3}{4}+\f rac{C}{t}$??

--Chris

3. You have got it damn right.Actually instead of asking us you can check it out yourself by differentiating what you have obtained.