Which of the following statements are true?
I. A linear equation $\frac{dy}{dx} + Py = Q$ has general solution $y\,e^{\int P\,dx} = \int Q\,e^{\int P\,dx}\,dx + C$ .
II. The constant $C$ is added after integrating the right side, not to the factor.
III. The integrating factor needs its own constant of integration.
IV. If $Q = 0$ , the equation also has separable variables.

All four: I, II, III and IVCorrect answerYour answerI, II and IV onlyCorrect answerYour answerI and II onlyCorrect answerYour answerI and IV onlyCorrect answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer B

Correct answer: B

I is the solution formula, II is how it is used, and IV holds: $\frac{dy}{y} = -P\,dx$ .
III is false: any one integrating factor works, so its constant is left out.

Worth noting

A constant in the factor would only scale both sides of the equation.

Concept: The method for linear equations
Typical timeTypical: 120 s
Your timeYours: —

The rule this testsSolving linear equations

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Ten questions from Homogeneous & Linear Differential Equations, at your own pace.

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