What is the general solution of dy/dx + 2y = 4?

Homogeneous & Linear Differential Equations · Question 90 of 120

Question 90

EasyOriginal question

What is the general solution of $\frac{dy}{dx} + 2y = 4$ ?

y = 4 + Ce^{-2x}

Correct answerYour answer

y = 2 + Ce^{2x}

Correct answerYour answer

y = 2x + C

Correct answerYour answer

y = 2 + Ce^{-2x}

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer D

Correct answer: D

The factor is $e^{2x}$ : $\frac{d}{dx}(ye^{2x}) = 4e^{2x}$ , so $ye^{2x} = 2e^{2x} + C$ .
$y = 2 + Ce^{-2x}$ .

Worth noting

$4 + Ce^{-2x}$ forgets to divide 4 by $P = 2$ ; the steady value is where $2y = 4$ .

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

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