Specialist2024 Exam 2 Section A · Q7CAS active1 mark

Separating variables in a differential equation

A solution to the differential equation

$\frac{dy}{dx} = e^{x-y}\left(\cos(x-y) - \cos(x+y)\right)$ can be found using

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\int e^{y}\cos(y)\,dy = 2\int e^{x}\cos(x)\,dx

\int \frac{e^{y}}{\sin(y)}\,dy = 2\int e^{-x}\sin(x)\,dx

\int \frac{e^{y}}{\sin(y)}\,dy = 2\int e^{x}\sin(x)\,dx

\int e^{-y}\sin(y)\,dy = 2\int \frac{e^{x}}{\cos(x)}\,dx

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