Question

How do you do this question?

Answer 1

y = Ce⁻ᵗ − 7

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