Answer:
y = Ce⁻ᵗ − 7
Step-by-step explanation:
dy/dt = -y − 7
dy/dt = -1 (y + 7)
Separate the variables.
dy / (y + 7) = -1 dt
Integrate both sides.
ln│y + 7│= -t + C
Solve for y.
y + 7 = e⁻ᵗ⁺ᶜ
y + 7 = eᶜ e⁻ᵗ
eᶜ is another arbitrary constant, so:
y + 7 = Ce⁻ᵗ
y = Ce⁻ᵗ − 7
