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>
3x^2 - 12 = 0
Personally, I would divide each side by 3 x^2 - 4 = 0
Then I would add 4 to each side x^2 = 4
Then I would take the square root of each side: x = +4
x = -4 .
Having found both solutions, I would relax with a cup of tea.
Answer:
f(x) = 2 ( x + 7/4)2 - 25/8
Step-by-step explanation:
Answer:
Step-by-step explanation:
378,903,970.
Answer:
1/2
Step-by-step explanation:
2/3 times 3/4 is 6/12, and 6/12 in simplest form is 1/2.
