Find the differential equation by eliminating arbitrary constants from the relation y = (c1 + c2x)ex - Mathematics and Statistics

Advertisements
Advertisements
Sum

Find the differential equation by eliminating arbitrary constants from the relation y = (c1 + c2x)ex 

Advertisements

Solution

y = (c1 + c2x)ex 

∴ ye–x = c1 + c2x

Differentiating w.r.t. x, we get

`y(-"e"^-x) + "e"^-x ("d"y)/("d"x)` = 0 + c2

∴ `"e"^x (("d"y)/("d"x) - y)` = c2

 Again, differentiating w.r.t. x, we get

`"e"^-x (("d"^2y)/("d"x^2) - ("d"y)/("d"x)) - "e"^-x (("d"y)/("d"x) - y)` = 0

∴ `"e"^-x (("d"^2y)/("d"x^2) - ("d"y)/("d"x) - ("d"y)/("d"x) + y)` = 0

∴ `("d"^2y)/("d"x^2) - 2("d"y)/("d"x) + y` = 0

Concept: Formation of Differential Equation by Eliminating Arbitary Constant
  Is there an error in this question or solution?
Chapter 1.8: Differential Equation and Applications - Q.4
Share
Notifications



      Forgot password?
Use app×