Specialist2026 NHT Exam 2 Section A · Q11CAS active1 mark

Separation of variables with trigonometric identities

By separation of variables, the differential equation $\dfrac{dy}{dx} = \dfrac{e^{x+y}\sin(2x)}{\sin(x+y) - \sin(x)\cos(y)}$ leads to

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

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

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

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

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