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Homogeneous & Linear Differential Equations · Question 71 of 120

Question 71

MediumOriginal question

What is the integrating factor of xdydx−y=x2x\frac{dy}{dx} - y = x^{2}?

Options for question 71

Show the answer and explanation
CorrectNot quiteAnswer B

Correct answer: B

Explanation

  1. In the form dydx+Py=Q\frac{dy}{dx} + Py = Q, P=−1xP = - \frac{1}{x}.

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

Worth noting

xx skips dividing through by xx first: then P=−1xP = -\frac{1}{x} and the factor is 1x\frac{1}{x}.

Concept
The integrating factor
Typical time
90 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.