Question

What is the integrating factor for \[\frac{dx}{dy}+P_{1}x=Q_{1}\]?

Options

• \[e^{\int Q_{1}\,dy}\]

• \[e^{-\int P_{1}\,dy}\]

• \[e^{\int P_{1}\,dx}\]

• \[e^{\int P_{1}\,dy}\]

Answer 1

For \[\frac{dx}{dy}+P_{1}x=Q_{1}\], the integrating factor is \[e^{\int P_{1}\,dy}\]. The integration is with respect to \[y\] because \[P_{1}\] is a function of \[y\].