Question

The general solution of \( \frac{dy}{dx} + y = 5 \) is:

• A. \( -\log|5 - y| = x + C \)
• B. \( -\log|5 - y| = e^x + C \)
• C. \( (5 - y)^2 = 2x + C \)
• D. \( y = \log|x| + C \)
• E. \( \log|x| + C \)

Hint:

For first-order linear differential equations, try to separate the variables and integrate both sides.

Answer 1

The Correct Option is A

The differential equation \( \frac{dy}{dx} + y = 5 \) is separable. 
Solving: \[ \frac{dy}{dx} = 5 - y \] \[ \frac{1}{5 - y} dy = dx \] Integrating both sides gives \( -\log|5 - y| = x + C \).