The answer for your question question is 3+ 16/3 i
This is a linear differential equation of first order. Solve this by integrating the coefficient of the y term and then raising e to the integrated coefficient to find the integrating factor, i.e. the integrating factor for this problem is e^(6x).
<span>Multiplying both sides of the equation by the integrating factor: </span>
<span>(y')e^(6x) + 6ye^(6x) = e^(12x) </span>
<span>The left side is the derivative of ye^(6x), hence </span>
<span>d/dx[ye^(6x)] = e^(12x) </span>
<span>Integrating </span>
<span>ye^(6x) = (1/12)e^(12x) + c where c is a constant </span>
<span>y = (1/12)e^(6x) + ce^(-6x) </span>
<span>Use the initial condition y(0)=-8 to find c: </span>
<span>-8 = (1/12) + c </span>
<span>c=-97/12 </span>
<span>Hence </span>
<span>y = (1/12)e^(6x) - (97/12)e^(-6x)</span>
x over 5 becuase the top and bottom are both divisible by 8 so you do that.
Answer:
10x+3
Step-by-step explanation:
or ![\frac{7\pi }{4}](https://tex.z-dn.net/?f=%5Cfrac%7B7%5Cpi%20%7D%7B4%7D)
divide both sides by 2
sinΘ = - ![\frac{\sqrt{2} }{2}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%7B2%7D%20%7D%7B2%7D)
Since the sin ratio is negative then Θ is in third / fourth quadrants
Θ =
(
) =
related acute angle
Θ = ( π +
) = ![\frac{5\pi }{4}](https://tex.z-dn.net/?f=%5Cfrac%7B5%5Cpi%20%7D%7B4%7D)
or Θ = ( 2π -
) = ![\frac{7\pi }{4}](https://tex.z-dn.net/?f=%5Cfrac%7B7%5Cpi%20%7D%7B4%7D)