Question:
The integrating factor of the linear DE \(\dfrac{dy}{dx}+\dfrac{2}{x}y=5x^{2}\) is
The integrating factor of the linear DE \(\dfrac{dy}{dx}+\dfrac{2}{x}y=5x^{2}\) is
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For \(y'+\dfrac{m}{x}y=\ldots\), IF is \(x^{m}\).
Updated On: Oct 17, 2025
- \(\dfrac{2}{x}\)
- \(2e^{x}\)
- \(2\log x\)
- \(x^{2}\)
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The Correct Option is D
Solution and Explanation
Standard form \(y'+P(x)y=Q(x)\) has IF \(=\exp\!\left(\int P(x)\,dx\right)\).
Here \(P(x)=\dfrac{2}{x}\). So
\[
\text{IF}=\exp\!\left(\int \frac{2}{x}dx\right)=\exp(2\ln x)=e^{\ln x^{2}}=x^{2}.
\]
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