The variables $x$ and $y$ are related by the differential equation $\frac{{{\mathrm{d}}^{2}}y}{\math

Question

The variables $x$ and $y$ are related by the differential equation $\frac{{{\mathrm{d}}^{2}}y}{\mathrm{d}{{x}^{2}}}=2{{\mathrm{e}}^{-2x}}$ Solve the differential equation. Hence find a possible solution curve that has an oblique asymptote, and state the equation of the oblique asymptote. [4]

Accepted Answer

Hence a possible solution curve with an oblique asymptote is $y=\frac{1}{2}{{\mathrm{e}}^{-2x}}+x+1$, where $C=1$, $D=1$. Oblique asymptote is ${y=x+1}$.

2023 HCI P1 Q1

2023 HCI P1 Q1

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