For x > 0 and 0 < y < π, match each equation in List I with its integrating factor in List II.

For x > 0 and 0 < y < π, match each equation…

Question 84

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For $x > 0$ and $0 < y < \pi$ , match each equation in List I with its integrating factor in List II.

List I	List II
A. $x\frac{dy}{dx} + 4y = 1$	I. $e^{- 3 x}$
B. $\frac{dy}{dx} - 3y = x$	II. $\sin y$
C. $(x + 1)\frac{dy}{dx} + y = 1$	III. $x^{4}$
D. $\frac{dx}{dy} + x\cot y = 1$	IV. $x + 1$

A-III, B-I, C-IV, D-IICorrect answerYour answerA-I, B-III, C-IV, D-IICorrect answerYour answerA-III, B-I, C-II, D-IVCorrect answerYour answerA-I, B-III, C-II, D-IVCorrect answerYour answer

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CorrectNot quiteAnswer A

Correct answer: A

A: divide by $x$ , $P = \frac{4}{x}$ , factor $x^{4}$ . B: $P = -3$ , factor $e^{-3x}$ .
C: $P = \frac{1}{x + 1}$ , factor $x + 1$ . D: linear in $x$ with $P_{1} = \cot y$ , factor $e^{\log \sin y} = \sin y$ .

Concept: The integrating factor
Typical timeTypical: 120 s
Your timeYours: —

The rule this testsLinear equations and the integrating factor

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

Practise this chapter →

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

Question 84

Explanation