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Homogeneous & Linear Differential Equations · Question 67 of 120

Question 67

EasyOriginal question

What is the integrating factor of dydx=x+y\frac{dy}{dx} = x + y?

Options for question 67

Show the answer and explanation
CorrectNot quiteAnswer A

Correct answer: A

Explanation

  1. In standard form, dydx−y=x\frac{dy}{dx} - y = x, so P=−1P = -1.

  2. The factor is e∫−1 dx=e−xe^{\int -1\,dx} = e^{-x}.

Worth noting

exe^{x} reads P=+1P = +1 off dydx=x+y\frac{dy}{dx} = x + y; moving yy to the left makes it −1-1.

Concept
The integrating factor
Typical time
60 s
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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.