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>
Answer:
45
Step-by-step explanation:
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Answer:
The answer to your question is: d = 0.85 units
Step-by-step explanation:
Data
Line equation: 1.2 x − 0.5 y + 1.1 = 0 A = 1.2; B = -0.5; C = 1.1
Point (0, 0) x = 0; y = 0
Formula
d = | Ax + By + C | / √(A² + B²)
Process
d = |(1.2)(0) + (-0.5)(0) + 1.1 | / √ (1.2)² + (0.5)²
d = | 1.1 | / √ 1.44 + 0.25
d = 1.1 / √ 1.69
d = 1.1 / 1.3
d = 0.85 units
Answer: Yes it is!
Step-by-step explanation:
Answer:
the value of x is 116
Step-by-step explanation:
180-64=116
