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Homogeneous & Linear Differential Equations · Question 97 of 120

What is the general solution for A?

Question 97

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 general solution for $A$ ?

A = Ce^{t/20} + 2{,}40{,}000

Correct answerYour answer

A = Ce^{-t/20} - 2{,}40{,}000

Correct answerYour answer

A = Ce^{t/20} - 600

Correct answerYour answer

A = Ce^{t/20} - 2{,}40{,}000

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer D

Correct answer: D

$\frac{d}{dt}\left(Ae^{-t/20}\right) = 12{,}000e^{-t/20}$ , so $Ae^{-t/20} = -2{,}40{,}000e^{-t/20} + C$ .
Multiply by $e^{t/20}$ : $A = Ce^{t/20} - 2{,}40{,}000$ .

Worth noting

$+2{,}40{,}000$ loses the minus sign of $\int e^{-t/20}\,dt = -20e^{-t/20}$ .

Concept: Solving a linear equation
Typical timeTypical: 90 s
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