Question

How do I solve this?

Answer 1

Answer:

Thus the solution of the differential becomes

\frac{y-5}{y+5}=e^{10x-20}

Step-by-step explanation:

Answer 2

Answer with Step-by-step explanation:

The given differential euation is

$\frac{dy}{dx}=(y-5)(y+5)\\\\\frac{dy}{(y-5)(y+5)}=dx\\\\(\frac{A}{y-5}+\frac{B}{y+5})dy=dx\\\\\frac{1}{100}\cdot (\frac{10}{y-5}-\frac{10}{y+5})dy=dx\\\\\frac{1}{100}\cdot \int (\frac{10}{y-5}-\frac{10}{y+5})dy=\int dx\\\\10[ln(y-5)-ln(y+5)]=100x+10c\\\\ln(\frac{y-5}{y+5})=10x+c\\\\\frac{y-5}{y+5}=ke^{10x}$

where

'k' is constant of integration whose value is obtained by the given condition that y(2)=0\\

$\frac{0-5}{0+5}=ke^{20}\\\\k=\frac{-1}{e^{20}}\\\\\therefore k=-e^{-20}$

Thus the solution of the differential becomes

 $\frac{y-5}{y+5}=e^{10x-20}$