What is the general solution of dy/dx - y = 2?

Homogeneous & Linear Differential Equations · Question 93 of 120

Question 93

EasyOriginal question

What is the general solution of $\frac{dy}{dx} - y = 2$ ?

y = Ce^{x} - 2

Correct answerYour answer

y = Ce^{x} + 2

Correct answerYour answer

y = Ce^{-x} - 2

Correct answerYour answer

y = 2x + Ce^{x}

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Show the answer and explanation

CorrectNot quiteAnswer A

Correct answer: A

The factor is $e^{-x}$ : $\frac{d}{dx}(ye^{-x}) = 2e^{-x}$ , so $ye^{-x} = -2e^{-x} + C$ .
$y = Ce^{x} - 2$ .

Worth noting

$Ce^{x} + 2$ loses the minus sign from $\int 2e^{-x}\,dx = -2e^{-x}$ .

Ten questions from Homogeneous & Linear Differential Equations, at your own pace.

Ten questions from Homogeneous & Linear Differential Equations, at your own pace.