Solve the first-order differential equations: (x2+1)dydx=xy

Annette Sabin

Annette Sabin

Answered

2022-01-22

Solve the first-order differential equations:
(x2+1)dydx=xy

Answer & Explanation

Ana Robertson

Ana Robertson

Expert

2022-01-22Added 26 answers

Solution:
(x2+1)dydx=xy
  1ydy=(xx2+1)dx
This is a separable linear first order differential which is of the form
N(y)dy=M(x)dx
  1ydy=xx2+1dx
Intagrating both sides
1ydy=xx2+1dx
Let x2+1=u
  2xdx=du
  xdx=12du
So,
  ln(y)=12udu=12udu
  ln(y)=12ln(u)+c
  ln(y)=12ln(x2+1)+c
  ln(y)=ln(x2+1)12+ln(ec)
  ln(y)=ln(ec(x2+1)12)
  y=ec(x2+1)12
  y(x)=cx2+1
 y(x)=cx2+1

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