Step-by-step explanation:
4x + 2xy=
4×4 + 2×4×-3
= 16 + (-24)
= - 8
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:
-24.8 m/s
Step-by-step explanation:
Given:
y₀ = 60 m
y = 40 m
v₀ = 15 m/s
a = -9.8 m/s²
Find: v
There are three constant acceleration equations we can use:
y = y₀ + v₀ t + ½ at²
v = at + v₀
v² = v₀² + 2a(y − y₀)
We aren't given the time, so we need to use the third equation, which is independent of time:
v² = v₀² + 2a(y − y₀)
Plug in the values:
v² = (15 m/s)² + 2(-9.8 m/s²) (40 m − 60 m)
v² = 617 m²/s²
v ≈ ±24.8 m/s
Since the coin is on the way down, the velocity is negative. So v = -24.8 m/s.
