It is given that $x\frac{\mathrm{d}y}{\mathrm{d}x}=2y-8$. Using the substitution $y=u{{x}^{2}}$ or o

Question

It is given that $x\frac{\mathrm{d}y}{\mathrm{d}x}=2y-8$. Using the substitution $y=u{{x}^{2}}$ or otherwise, solve the differential equation giving your answer in the form $y=\mathrm{f}\left( x ight)$. [4] Given that $y>3$ when $x=1$, show that $y>4-{{x}^{2}}$ for $x
e 0$. [2]

Accepted Answer

(i) $y=Cx^2+4$; (ii) $y>4-x^2$ for $x\ne0$

2021 DHS Promo Q3

2021 DHS Promo Q3

Video Solution:

Solution:

Solution locked