Exercise · ZW-INTEGRATING-FACTOR-010 · ★★★ Advanced

When computing \(\int p\,dx\) for the integrating factor, the constant of integration is dropped. Why is that allowed?

Choose one option.

Show answer

C. Because the constant only multiplies \(\mu\) and cancels when solving for \(y\)

Explanation

With \(c\) in the integral, \(\mu\) is multiplied by \(e^{c}\), a factor that appears on both sides of \((\mu y)'=\mu q\) and cancels. Any antiderivative works.

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Review the concept: Integrating factor

An integrating factor is a function \(\mu\) that, when multiplied by a first-order linear equation with coefficient \(p\), turns the left side into the derivative of a product.

\[\mu(x)=e^{\int p(x)\,dx}\]

When computing \(\int p\,dx\) for the integrating factor, the constant of integration is dropped. Why is that allowed?

Explanation

Review the concept: Integrating factor

More practice problems: integrating factor