In the standard form dy/dx + Py = Q, what are P and Q for xdy/dx - 3y = x^4e^x?

Question 76

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In the standard form $\frac{dy}{dx} + Py = Q$ , what are $P$ and $Q$ for $x\frac{dy}{dx} - 3y = x^{4}e^{x}$ ?

P = -3

Q = x^{4}e^{x}

Correct answerYour answer

P = \frac{3}{x}

Q = x^{3}e^{x}

Correct answerYour answer

P = -\frac{3}{x}

Q = x^{3}e^{x}

Correct answerYour answer

P = -\frac{3}{x}

Q = x^{4}e^{x}

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer C

Correct answer: C

Divide through by $x$ , the coefficient of $\frac{dy}{dx}$ : $\frac{dy}{dx} - \frac{3}{x}y = x^{3}e^{x}$ .
So $P = -\frac{3}{x}$ and $Q = x^{3}e^{x}$ .

Worth noting

$P = -3$ , $Q = x^{4}e^{x}$ reads the equation before dividing by $x$ , the coefficient of $\frac{dy}{dx}$ .

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