The integrating factor of $x \frac{d y}{d x}+3 y=x^2$ is

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Aicharya · Accepted Answer

Given equation is, $x \frac{d y}{d x}+3 y=x^2 \text { or } \frac{d y}{d x}+\frac{3}{x} \cdot y=x$ Comparing with, $\frac{d y}{d x}+P y=Q,$ We have $p=\frac{3}{x}$ and So, the integrating factor is, $\mathrm{IF}=e^{\int p d x}=e^{\int \frac{3}{x} d x}=e^{3 \log x}=e^{\log x^3}=x^3$ $r=\frac{d^{\prime}}{2}=\frac{0.8}{2}=0.4 \mathrm{~mm}=4 \times 10^{-4} \mathrm{~m}$ Hence, $\Delta l=\frac{m g l}{\pi r^2 Y}=\frac{10 \times 10 \times 3}{\pi \times\left(4 \times 10^{-4}\right)^2 \times 10^{11}}$ $=5.96 \times 10^{-3} \mathrm{~m}=0.596 \mathrm{~cm} \simeq 0.6 \mathrm{~cm}$

The integrating factor of \(x \frac{d y}{d x}+3 y=x^2\) is

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