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Homogeneous & Linear Differential Equations · Question 96 of 120

What is the integrating factor of this equation?

Question 96

EasyOriginal question

A savings account earns interest at 5% a year, compounded continuously, and money is paid in continuously at the rate of ₹12,000 a year. The balance $A$ (in rupees) after $t$ years satisfies $\frac{dA}{dt} = \frac{A}{20} + 12{,}000$ .

What is the integrating factor of this equation?

e^{t/20}

Correct answerYour answer

e^{-20t}

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e^{-t/20}

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e^{-t}

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Show the answer and explanation

CorrectNot quiteAnswer C

Correct answer: C

In standard form, $\frac{dA}{dt} - \frac{1}{20}A = 12{,}000$ , so $P = -\frac{1}{20}$ .
The factor is $e^{\int -\frac{1}{20}\,dt} = e^{-t/20}$ .

Worth noting

$e^{t/20}$ reads $P = +\frac{1}{20}$ ; moving $\frac{A}{20}$ to the left makes it negative.

Concept: The integrating factor
Typical timeTypical: 90 s
Your timeYours: —

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