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.
Keep practising Differential Equations
Browse all Differential Equations questions for AP Intermediate 2nd Year, or explore more Mathematics topics.
Related questions
For the linear DE dy/dx + (1/x)y = x, the INTEGRATING FACTOR μ(x) is:Complete the definition of order and degreeComplete the definition of a differential equationOrder, degree, or neither?True or false: methods of solutionRecognising the typeGeneral solution or particular solution?True or false: what a solution is