Question:
The integrating factor of the differential equation $\frac{dy}{dx}-2y=2x-3$ is ________.
The integrating factor of the differential equation $\frac{dy}{dx}-2y=2x-3$ is ________.
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I.F. $= e^{\int P dx}$.
Updated On: Jun 26, 2026
- $e^{2x}$
- $-\frac{1}{2}e^{-2x}$
- $\frac{1}{2}e^{-2x}$
- $\frac{1}{2}e^{-2x}$ (Duplicate)
- $e^{-2x}$
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The Correct Option is
Solution and Explanation
Step 1: Concept
For a linear differential equation $\frac{dy}{dx} + Py = Q$, the Integrating Factor (I.F.) is $e^{\int P dx}$.
Step 2: Meaning
Here, $P = -2$.
Step 3: Analysis
I.F. $= e^{\int -2 dx} = e^{-2x}$.
Step 4: Conclusion
The integrating factor is $e^{-2x}$. Final Answer: (E)
For a linear differential equation $\frac{dy}{dx} + Py = Q$, the Integrating Factor (I.F.) is $e^{\int P dx}$.
Step 2: Meaning
Here, $P = -2$.
Step 3: Analysis
I.F. $= e^{\int -2 dx} = e^{-2x}$.
Step 4: Conclusion
The integrating factor is $e^{-2x}$. Final Answer: (E)
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