alleryFor the linear DE dy/dx + (1/x)y = x, the INTEGRATING FACTOR μ(x) is:
A$e^x$ (always the exponential)
B$1/x$ (the reciprocal)
C$\ln(x)$ (the logarithm)
D$x$ (since $e^{\int 1/x \, dx} = x$)
Answer & Solution
Correct answer: D. $x$ (since $e^{\int 1/x \, dx} = x$)
IF μ = e^(∫P dx) = e^(∫(1/x) dx) = e^(ln|x|) = |x|. For x > 0, μ = x.
**Multiply DE by x:** derivative of (xy) = x²
integrate to get xy = x³/3 + C.
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