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Homogeneous & Linear Differential Equations · Question 91 of 120

What is its integrating factor?

Question 91

EasyOriginal question

Consider the linear differential equation dydx+2xy=2x\frac{dy}{dx} + 2xy = 2x.

What is its integrating factor?

Options for question 91

Show the answer and explanation
CorrectNot quiteAnswer C

Correct answer: C

Explanation

  1. P=2xP = 2x, so ∫P dx=x2\int P\,dx = x^{2}.

  2. The factor is ex2e^{x^{2}}.

Worth noting

e2xe^{2x} puts PP itself in the exponent instead of ∫P dx\int P\,dx.

Concept
The integrating factor
Typical time
90 s
Your time
—
The rule this testsSolving linear equations
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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.