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Homogeneous & Linear Differential Equations · Question 69 of 120

Question 69

MediumOriginal question

What is the integrating factor of dxdy+xy=y2\frac{dx}{dy} + \frac{x}{y} = y^{2}, linear in xx?

Options for question 69

Show the answer and explanation
CorrectNot quiteAnswer C

Correct answer: C

Explanation

  1. Here xx is the unknown: dxdy+Px=Q\frac{dx}{dy} + Px = Q with P=1yP = \frac{1}{y}.

  2. The factor is e∫1ydy=ye^{\int \frac{1}{y}dy} = y.

Worth noting

xx is the unknown here; the factor is a function of yy.

Concept
The integrating factor for \(\frac{dx}{dy} + Px = Q\)
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.