Question

How do I solve this?

Solve y′=(y−5)(y+5) if y(2)=0?

I used methods of separation and did a partial fraction integral and ended up with

(ln(y+5)-ln(y-5))/10 = x

I'm not sure if I did this correctly nor do I know how to solve for y at this point. Please send help! Thank you.

Answer 1

Thus the solution of the differential becomes

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

Explanation:

Answer 2

Answer with Step-by-step explanation:

The given differential euation is

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

where

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

`(0-5)/(0+5)=ke^(20)\\\\k=(-1)/(e^(20))\\\\\therefore k=-e^(-20)`

Thus the solution of the differential becomes

`(y-5)/(y+5)=e^(10x-20)`