This can be factored as a difference of two squares. When you have a difference of two squares (a² - b²), it will factor out into (a + b) (a - b).
(x² - r²)
(x + r)(x - r)
You can multiply the two groups to double check it.
(x + r)(x - r)
x² - rx + rx - r²
x² - r²
We rearrange the given differential equation to combine all the y terms on the left side of the equation and the x terms on the right side:
[(1 + y^2) / y] dy = cos(x) dx
[(1/y) + y] dy = cos(x) dx
We integrate both sides to get
ln y + (y^2 / 2) = sin(x) + C
Then, we apply the initial condition y = 1 at x = 0 to get the value of C:
ln (1) + (1^2 / 2) = sin(0) + C
C = ln (1) + (1^2 / 2) - sin(0)
C = 1/2
Therefore, our final answer is
ln (y) + (y^2 / 2) = sin(x) + 1/2
Answer=3610.201
3*1000=3,000
6*100=600
1*10=10
2*1/10=0.2
1*1/1000=0.001
3000+600+10+0.2+0.001=3610.201
Ummm is this a full question?