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Homogeneous & Linear Differential Equations · Question 64 of 120

Question 64

EasyOriginal question

What is the integrating factor of dydx+3y=x\frac{dy}{dx} + 3y = x?

Options for question 64

Show the answer and explanation
CorrectNot quiteAnswer D

Correct answer: D

Explanation

  1. In the form dydx+Py=Q\frac{dy}{dx} + Py = Q, P=3P = 3.

  2. The factor is e∫P dx=e3xe^{\int P\,dx} = e^{3 x}.

Worth noting

3x3x is ∫P dx\int P\,dx; the factor is e3xe^{3x}.

Concept
The integrating factor
Typical time
60 s
Your time
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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.