Mathematics 9709 · AS & A Level · Differential equations

Differential equations — practice question

(i)[2]

Write $\frac{1}{x(2x + 3)}$ as a partial fraction decomposition.

(ii)[7]

The variables $x$ and $y$ obey the differential equation $x(2x + 3)\frac{dy}{dx} = y$, and it is stated that $y = 1$ when $x = 1$. Solve the differential equation and determine $y$ when $x = 9$, expressing your answer correct to 3 significant figures.

Worked solution & mark scheme

This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Use a suitable method to find $A$ and $B$ so that $\frac{1}{x(2x+3)}=\frac{A}{x}+\frac{B}{2x+3}$, or an equivalent form” …

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