Question:
The general solution of \( \frac{dy}{dx} + y = 5 \) is:
The general solution of \( \frac{dy}{dx} + y = 5 \) is:
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For first-order linear differential equations, try to separate the variables and integrate both sides.
Updated On: Apr 7, 2026
- \( -\log|5 - y| = x + C \)
- \( -\log|5 - y| = e^x + C \)
- \( (5 - y)^2 = 2x + C \)
- \( y = \log|x| + C \)
- \( \log|x| + C \)
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The Correct Option is A
Solution and Explanation
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 \( -\log|5 - y| = x + C \).
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