math- differential equations

posted by .

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 -

    hello i am retada and i love u

  • please answer! -

    retada i believe that was unecessary

  • math- differential equations -

    (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)

    Differentiate again:

    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 -

    ok thanks

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. math

    how do you isolate a variable? my teacher gave us questions and we are suppose to isolate the variable x PLEASE HELP! x + 3y = 11 You isolate it by moving everyting to the other side except that variable. Thus x + 3y = 11 is the same
  2. Math HURRY !!!!!!!!

    There are two bikes one with normal wheels and one with regular hexagon shaped wheels. Imagine you put a reflector on the front wheel of each bike. You stood on the side while the bikes are ridden past you you watch the reflector's …
  3. math

    If the answer is 1-2/3m what is the question> How can you solve equations like these?
  4. Differential Equations

    Find the general solution of the differential equation specified. 1) dy/dt= 1/(ty+1+y+1) 2) dy/dx=sec y I got y(x)=arcsin(x) for the second one. I'm not sure what to do with the first one.
  5. math

    2x+3y=6 (solve for x) 2x+3y=6 Get unknown on one side and everything else on the other side. To do this we ned to move 3y. How to do that?
  6. algebra

    I cant get this one nither I tried like 4 times to get right answer. 5x+12-3x=-2x-13-x x=-5 5x+12-3x=-2x-13-x First, let's get the unknowns on one side of the equation and the knowns on the other side. 5x - 3x + 2x + x = -12 - 13 5 …
  7. calculus

    is y = x^3 a solution to the differential equation xy'-3y=0?
  8. Algebra

    Okay, i need help. I'm solving linear equations in intermediate algebra. My problem is that I never know which number to subtract first. Ex: 5y-8=-18 To get the right answer (-2), they move they add the 8 to both sides. But on 27w-64=-37 …
  9. Math

    A two population model is satisfied by a system of differential equations given by, V(x,y) = (ax,by)^T The general solution of the system of differential equations has x = áe^at for some constant á. The parameter t can be eliminated …
  10. Differential Equations!

    I'm struggling solving this separable differential equations: (du/dv) = ((uv+u)/(uv+v)) I multiplied both sides by dv to get on the left side just du and cancel out dv, but after that don't know where to go. I've tried integration …

More Similar Questions