2020 TMJC P1 Q8
(i)
Show that the differential equation $\frac{\text{d}y}{\text{d}x}=5\left( x-y \right)$ may be reduced by the substitution $w=x-y$ to $\frac{\text{d}w}{\text{d}x}=1-5w$. Hence find the general solution for $~y$ in terms of $x$.
[6]
(ii)
Find the particular solution of the differential equation $\frac{\text{d}y}{\text{d}x}=5\left( x-y \right)$ when $x=0$ and $y=-1$.
[2]
(iii)
Sketch the graph of the particular solution found in part (ii), showing clearly the behaviour of the graph as $x\to \infty $, the coordinates of the axial intercept(s) and equations of any asymptote(s).
[3]
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