# Thread: Integrating to Find Particular Solution

1. ## Integrating to Find Particular Solution

Firstly,

I keep getting a LaTex Error with the following equation:
y=\int(x+\frac{20}{x^2}+\frac{5}{x^2})dx

Secondly, my teacher said the answer to the following question is c=3.9, but I keep getting a different answer:

Integrate the following equation to find the particular solution
y= integral of (x + 20/x^3 + 5/x^2)dx, where x = 3 and y = 9
Here is my working:

y = [(x^2)/2] + [(20x^-2)/-2] + [(5x^-1)/-1] + C

y = [(x^2)/2] - (10x^-2) - (5x^-1) + C

y = [(x^2)/2] - (10/x^2) - (5/x) + C

9 = [(3^3)/2] - (10/3^2) - 5/3 + C

9 = 4.5 - 1.1 - 1.6 + C

9 - 4.5 + 1.1 + 1.6 = c

C = 7.2 (My teacher's answer is C=3.9)

What did I do wrong with LaTex, and this answer?

2. Certainly

3. Originally Posted by sparky
Firstly,

I keep getting a LaTex Error with the following equation:
y=\int(x+\frac{20}{x^2}+\frac{5}{x^2})dx

Secondly, my teacher said the answer to the following question is c=3.9, but I keep getting a different answer:

Here is my working:

y = [(x^2)/2] + [(20x^-2)/-2] + [(5x^-1)/-1] + C

y = [(x^2)/2] - (10x^-2) - (5x^-1) + C

y = [(x^2)/2] - (10/x^2) - (5/x) + C

9 = [(3^3)/2] - (10/3^2) - 5/3 + C

9 = 4.5 - 1.1 - 1.6 + C
3^2= 27, not 9, so3^2/2= 12.5, not 4.5.

9 - 4.5 + 1.1 + 1.6 = c

C = 7.2 (My teacher's answer is C=3.9)

What did I do wrong with LaTex, and this answer?

4. Sorry, 9 = [(3^3/2] - (10/3^2) - 5/3 + C

is supossed to be 2, my mistake:

y = [(x^2)/2] - (10/x^2) - (5/x) + C

9 = [(3^2)/2] - (10/3^2) - 5/3 + C

9 = 4.5 - 1.1 - 1.6 + C

9 - 4.5 + 1.1 + 1.6 = c

C = 7.2

Originally Posted by FernandoRevilla
Certainly

Yes, this is what I got as well. So what is the correct answer?

5. Originally Posted by sparky
Sorry, 9 = [(3^3/2] - (10/3^2) - 5/3 + C

is supossed to be 2, my mistake:

y = [(x^2)/2] - (10/x^2) - (5/x) + C

9 = [(3^2)/2] - (10/3^2) - 5/3 + C

9 = 4.5 - 1.1 - 1.6 + C

9 - 4.5 + 1.1 + 1.6 = c

C = 7.2

Yes, this is what I got as well. So what is the correct answer?
Making my calculator do all the work so I'm not making a trivial numerical error, I get 7.2.

-Dan