Posted by manny on Friday, September 7, 2007 at 7:23pm.
This is what im given
(1 + x)dy/dx - xy = x + x2
From my understanding I should move everything to one side like:
(1 + x)dy/dx -xy - x -x2 = 0
then dy/ dx = xy + x + x2/(1 + x)
and from here i am lost
Can you guys help!
- math- differential equations - retada, Friday, September 7, 2007 at 7:30pm
hello i am retada and i love u
- please answer! - manny, Friday, September 7, 2007 at 8:05pm
retada i believe that was unecessary
- math- differential equations - Count Iblis, Friday, September 7, 2007 at 8:23pm
(1 + x)dy/dx - xy = x + x^2 --->
y' - x/(1+x) y = x
First solve the homogeneous part of the equation:
y_h' - x/(1+x) y_h =0 --->
y_h = A exp(x)/(1+x)
Then you promote A from a constant to a function of x and put:
y = A(x) Exp(x)/(1+x)
If you subsitute this in the differential equation, then only the term involving the derivative of A will survive. That's because the terms that do not involve the derivative of A are exactly what you get when you take y to be y_h. y_h satisfies the homogeneous equation and therefore they add up to zero.
So, we get:
A' Exp(x)/(1+x) = x --->
A' = x(1+x)Exp(-x)
Integral of Exp(ax) = 1/a Exp(ax)
Differentiate both sides w.r.t. a:
Integral of x Exp(ax) =
(x/a -1/a^2) Exp(ax)
Integral of x^2 Exp(ax) =
( x^2/a -2x/a^2 +2/a^3) Exp(ax)
We thus see that:
A(x) = (-3x -3 -x^2)Exp(-x) + const.
[Note: I didn't check if I made any errors in the calculations!]
- math- differential equations - manny, Friday, September 7, 2007 at 8:35pm
Answer This Question
More Related Questions
- math - how do you isolate a variable? my teacher gave us questions and we are ...
- calculus - is y = x^3 a solution to the differential equation xy'-3y=0?? how do ...
- Differential Equations! - I'm struggling solving this separable differential ...
- Math - A two population model is satisfied by a system of differential equations...
- Math HURRY !!!!!!!! - There are two bikes one with normal wheels and one with ...
- algebra - I cant get this one nither I tried like 4 times to get right answer. ...
- math - If the answer is 1-2/3m what is the question> How can you solve ...
- math - 2x+3y=6 (solve for x) 2x+3y=6 Get unknown on one side and everything else...
- Differential Equations - Find the general solution of the differential equation ...
- Algebra - Okay, i need help. I'm solving linear equations in intermediate ...