Solute the equation: \(\displaystyle{\left({1}-{x}^{{2}}\right)}{y}{''}={x}{y}'\)

jisu61hbke 2022-03-23 Answered
Solute the equation:
(1x2)y=xy
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Answers (1)

Avery Maxwell
Answered 2022-03-24 Author has 13 answers
The given equation is second order linear ordinary differential equation. This solution for the interval, |x|<1, there is another solution for |x|>1.
(1x2)y=xy
(1x2)ddx(y)=xy
d(y)dn=xy1x2
d(y)y=x1x2dx
Integrating dyy=x1x2dx
lny=12ln(1x2)+lnC [lnc constant]
y=c11x2
dy=c(dx)1x2
1cdy=dx1x2
1cy=sinx+d [d is constant]
sinx=ycd
x=sin(ycd)
Solution: x=sin(Ay+B), A=1c, B=d
|n|>1
y=cn21
dy=c(dx)n21
dy=cdxn21
y=cln|n+n21|+d c,d constant
Not exactly what you’re looking for?
Ask My Question

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

New questions