Study Pure Mathematics worksheet on Differential Equations for A-Level. Useful for revision, homework, and exam preparation in Zimbabwe.
A free account is needed to download. Sign in or create one
This is the A-Level Pure Mathematics worksheet from 2020. It is a free worksheet for revision.
Upper $6{ }^{\text {th }}$
LOCKDOWN PURE MATHS TEST 48
Monday 21 September 2020
25 MARKS ANSWER ALL QUESTIONS
***PRESENT YOUR WORK NEATI.Y***
NB: If a numerical answer cannot be given exactly, and the accuracy required is not specified in the question, then in the case of an angle it should be given to the nearest degree, and in other cases it should be given correct to $\mathbf{2}$ significant figures.
1. Given that $x^{2}+x y+y^{2}=12$, find $\frac{d y}{d x}$.
[4]
\[
\begin{array}{l}
x^{2}+x y+y^{2}=12
\Rightarrow 2 x+\left[x \frac{d y}{d x}+y(1)\right]+2 y \frac{d y}{d x}=0
\Rightarrow 2 x+x \frac{d y}{d x}+y+2 y \frac{d y}{d x}=0
\Rightarrow x \frac{d y}{d x}+2 y \frac{d y}{d x}=-(2 x+y)
\Rightarrow(x+2 y) \frac{d y}{d x}=-(2 x+y)
\Rightarrow \frac{d y}{d x}=-\frac{(2 x+y)}{x+2 y}
\end{array}
\]
2. Find the general solution of the differential equation $x y \frac{d y}{d x}+2-y^{2}=0$.
\[
\begin{array}{l}
x y \frac{d y}{d x}+2-y^{2}=0
\Rightarrow x y \frac{d y}{d x}=y^{2}-2
\end{array}
\]
STUDY while others are sleeping, WORK while others are loafing, PREPARE while others
are playing, and You will ENJOY while others are REGRETTING.
Page 1
© Tarakino N.P. 0772978155/0717267175
ntarakino@gmail.com