IB Maths AA HL AA 5.4 Differential equations and Maclaurin series questions

Exam-style questions in the shape of Paper 1 and Paper 2, with full markschemes. Read the markscheme, or type, photograph or draw your answer and get it marked.

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Question 1

Paper 1, no calculatorMedium6 marks

The positive solution $y$ of

\frac{dy}{dx}=\frac{2x}{y}

satisfies $y(1)=1$ for $1\leq x\leq 2$ An Euler estimate is made using a step length of $\frac12$

(a)

Write down the Euler estimate for $y\left(\frac32\right)$

[1]

(b)

Hence, write down the Euler estimate for $y(2)$

[1]

(c)

Determine the exact value of $y(2)$ by solving the differential equation.

[3]

(d)

Hence, state whether the estimate in (b) is an overestimate or an underestimate of the exact value. Justify your answer.

[1]

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