linear differential equations? (1 Viewer)

indeed · Sep 29, 2023

(from the James Ruse 2023 3 u paper)

(answers C btw)

Do you guys think this is necessary to know, the working involves using the below equation which i never learnt

scaryshark09 · Sep 29, 2023

indeed said:
(from the James Ruse 2023 3 u paper)
View attachment 40082(answers C btw)

Do you guys think this is necessary to know, the working involves using the below equation which i never learnt
View attachment 40083

wait this question is so hard, can someone explain

cossine · Sep 29, 2023

indeed said:
(from the James Ruse 2023 3 u paper)
View attachment 40082(answers C btw)

Do you guys think this is necessary to know, the working involves using the below equation which i never learnt
View attachment 40083

Luukas.2 · Sep 29, 2023

indeed said:
(from the James Ruse 2023 3 u paper)
View attachment 40082(answers C btw)

Do you guys think this is necessary to know, the working involves using the below equation which i never learnt
View attachment 40083

$\begin{align*} \text{A first order DE is linear in $y$ if it can be written as} \qquad f(x) \times \cfrac{dy}{dx} + g(x) \times y &= h(x) \qquad \text{where $f(x)$, $g(x)$, and $h(x)$ are not restricted as to degree} \\ \\ \text{Option (A) can be written as} \qquad 1 \times \cfrac{dy}{dx} + 0 \times y &= 2x^2 \qquad \text{and so fits the form to be linear in $y$} \\ \text{Option (B) can be written as} \qquad 1 \times \cfrac{dy}{dx} + -1 \times y &= x \qquad \text{and so fits the form to be linear in $y$} \\ \text{Option (D) can be written as} \qquad x \times \cfrac{dy}{dx} + -3 \times y &= 0 \qquad \text{and so fits the form to be linear in $y$} \\ \\ \text{Option (C) can be written as} \qquad 1 \times \cfrac{dy}{dx} + -3 \times y^2 &= 0 \qquad \text{but this is \emph{not} linear in $y$} \\ \text{as writing it as} \qquad 1 \times \cfrac{dy}{dx} + -3y \times y &= 0 \qquad \text{requires $g(x,\ \!y) = -3y$, a function of $x$ and $y$.} \end{align*}$

I wondered when I first saw this question, I have not seen anything like it in any other paper.

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linear differential equations? (1 Viewer)

indeed

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scaryshark09

∞∆ who let 'em cook dis long ∆∞

cossine

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Luukas.2

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