Read the two statements and choose the correct option. I. dy/dx + y/x = sin x has the integrating factor x. II. If I is an integrating factor, so is 5I.

Homogeneous & Linear Differential Equations · Question 72 of 120

Question 72

MediumOriginal question

Read the two statements and choose the correct option.
I. $\frac{dy}{dx} + \frac{y}{x} = \sin x$ has the integrating factor $x$ .
II. If $I$ is an integrating factor, so is $5I$ .

Only ICorrect answerYour answerOnly IICorrect answerYour answerBoth I and IICorrect answerYour answerNeither I nor IICorrect answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer C

Correct answer: C

I: $e^{\int \frac{dx}{x}} = e^{\log x} = x$ . True.
II: multiplying by $5I$ only scales both sides by 5, and the left side is still an exact derivative. True.

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

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