Further differential equations questions

Practice questions covering further differential equations from this specification. Attempt the questions below; real-paper references for this topic are being imported.

Questions to attempt

6 questions on Further differential equations, each with its mark scheme and worked method. Reveal the answer when you have had a go.

FP1-3.1 · Use of Taylor series method for series solution of differential equations.
Q1
ORIGINAL
Year 2
Year 2: this is content the exam board adds beyond the AS subject content, for the full A-level.
1.
Given that $\dfrac{\mathrm{d}y}{\mathrm{d}x}=x^2+y^2$ and $y=1$ at $x=0$ , find the series solution for $y$ as far as the term in $x^4$ .
(6)
(Total for Question 1 is 6 marks)
FP1-3.1 · Use of Taylor series method for series solution of differential equations.
Q2
ORIGINAL
Year 2
Year 2: this is content the exam board adds beyond the AS subject content, for the full A-level.
2.
Given that $\dfrac{\mathrm{d}y}{\mathrm{d}x}=x+y$ and $y=1$ at $x=0$ , find the series solution for $y$ in ascending powers of $x$ as far as the term in $x^3$ .
(4)
(Total for Question 2 is 4 marks)
FP1-3.1 · Use of Taylor series method for series solution of differential equations.
Q3
ORIGINAL
Year 2
Year 2: this is content the exam board adds beyond the AS subject content, for the full A-level.
3.
Given that $\dfrac{\mathrm{d}y}{\mathrm{d}x}=\sin(x+y)$ and $y=0$ at $x=0$ , find the series solution for $y$ as far as the term in $x^3$ .
(6)
(Total for Question 3 is 6 marks)
FP1-3.2 · Differential equations reducible by means of a given substitution.
Q4
ORIGINAL
Year 2
Year 2: this is content the exam board adds beyond the AS subject content, for the full A-level.
4.
Use the substitution $z=y^{-1}$ to find the general solution of $\dfrac{\mathrm{d}y}{\mathrm{d}x}+y=xy^{2}$ .
(6)
(Total for Question 4 is 6 marks)
FP1-3.2 · Differential equations reducible by means of a given substitution.
Q5
ORIGINAL
Year 2
Year 2: this is content the exam board adds beyond the AS subject content, for the full A-level.
5.
Use the substitution $z=y^{-1}$ to show that $\dfrac{\mathrm{d}y}{\mathrm{d}x}+y=xy^{2}$ reduces to $\dfrac{\mathrm{d}z}{\mathrm{d}x}-z=-x$ .
(3)
(Total for Question 5 is 3 marks)
FP1-3.2 · Differential equations reducible by means of a given substitution.
Q6
ORIGINAL
Year 2
Year 2: this is content the exam board adds beyond the AS subject content, for the full A-level.
6.
Use the substitution $y=vx$ to solve $\dfrac{\mathrm{d}y}{\mathrm{d}x}=\dfrac{x^{2}+y^{2}}{xy}$ given that $y=2$ when $x=1$ , and express $y$ in terms of $x$ .
(7)
(Total for Question 6 is 7 marks)

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Printable question pack — FP1-3 Further differential equations (Further Pure 1)All 20 questions across 2 specification points — 14 more than the 6 above — with the full mark scheme. Guest accessible · browser print.

FP1-3 Further differential equations (Further Pure 1) revision notes

Real-paper references

Real-paper references for this module are being imported — the questions above are the site's own, exam-faithful, marked.

Reference rows contain series, paper, question number, marks and classification metadata only. Pearson's question papers open on Pearson's own website.

Questions to attempt

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