CAPE Pure Mathematics Unit 2 · May/June 2008 (T&T) · Paper 2 · Question 2(a)(ii)
Solve the differential equation x^2 \frac{\mathrm{d}y}{\mathrm{d}x} + xy = \ln x.
The mark scheme is shown once you've answered.
Practise this questionOther parts of this question
- 2(a)(i)Find
\int \frac{1}{x} \ln x \, \mathrm{d}x.[3 marks] - 2(b)(i)Find the values of the constants
mandn, given thaty = m \cos x + n \sin xsatisfies the differential equation…[5 marks] - 2(b)(ii)Hence, find the general solution of the differential equation.[3 marks]
- 2(c)(i)Express
\frac{2 + 3x - x^2}{(x - 1)(x^2 + 1)}in partial fractions.[6 marks] - 2(c)(ii)Hence, find
\int \frac{2 + 3x - x^2}{(x - 1)(x^2 + 1)} \, \mathrm{d}x.[3 marks]
More practice: the rest of this paper · more Differential Equations and Modeling questions · all CAPE Pure Mathematics Unit 2 past papers