Expert: Paul Klarreich - 11/2/2008

Question
Find the general solution for dy/dx=x^3y
I can't find a way to separate the variables, so I'm at a loss as to what to do.

Answer

Questioner:   Marcus
Category:  Calculus
Private:  no
 
Subject:  integration (differential equation?)
Question:  Find the general solution for dy/dx=x^3y I can't find a way to separate the variables, so I'm at a loss as to what to do.
.................................
Hi Marcus,

How about separating the variables?
dy
-- = x^3 y
dx  

Divide by y, multiply by dx:

dy   
-- = x^3 dx
y    

ln y = x^4/4 + c.(small c)

etc

y = C e^(x^4/4)   (big C)

Check:

dy
-- = C x^3 e^(x^4/4)
dx
  
dy
-- = x^3 C e^(x^4/4)
dx

dy
-- = x^3 y
dx