Differential equations

(X+y) dx + xdy =0

  1. 👍 0
  2. 👎 0
  3. 👁 97
  1. (x+y)dx = -x dy

    -x dy /(x+y) dx = 1

    -x / [ x(1 +y/x)] dx = 1

    - dy /(1 +y/x) = dx

    Let u =y/x then xu = y so x du/dx + u = dy/dx.

    - (x du/dx + u) / ( 1+ u ) = 1

    x du/dx + u = -(1 + u)

    x du/dx + u = -1 - u

    x du/dx + 2u = -1

    (x/dx) du + 2u = -1

    x/dx + (2u)/du = -1/du

    x/dx = (-1 - 2u)/du

    du/(-1-2u) = dx/x

    (-1/2)log|-1 - 2u| = log|x| + C

    Multiplying by -2:

    log|-1-2u| = -2log|x| + C

    log|-1-2u| = log|1/x^2| + C

Respond to this Question

First Name

Your Response

Similar Questions

  1. maths help sir steve

    sir steve what about these i just solved it now i didnt get it if x^2+2xy+3y^2=1 prove that (x+3y)^3d^2y/dx^2+2(x^2+2xy+3y^2)=0 i solve with implicit derivative like these 2x+2(xdy/dx+y)+6ydy/dx=0 2x+2xdy/dx+2y+6ydy/dx=0

    asked by practising and need help on November 12, 2016
  2. maths

    xdy-ydx=sqrt(x^2-y^2)dx

    asked by ashely on February 11, 2012
  3. maths(Differential Equation)

    Solve the differential equation below (Y + y^3/3 + x^2/2)dx + 1/4(1 + y^2)xdy=0

    asked by BEN on March 3, 2016
  4. Linear Algebra

    Solve the initial value problem: xdy/dx+4y=7x^3-10x for y(1)=4

    asked by Brianna on September 14, 2012
  5. Calculus

    Find the particular solution that satisfies the intial condition: xdy - (2xe^(-y/x)+y)dx = 0

    asked by John on January 5, 2012
  6. maths

    solve the initial value problem of the differential equation (y+sqrt(x^2+y^2))dx-xdy=0,y(3)=4

    asked by Anonymous on October 1, 2016
  7. calculus

    If y is a differentiable function of x, then the slope of the tangent to the curve xy - 2y + 4y^2 = 6 at the point where y=1 is ...... How do I do this? Thanks. xy - 2y + 4y^2 = 6 ---> d[xy - 2y + 4y^2] = 0 ---> xdy + ydx - 2dy +

    asked by Jen on December 3, 2006
  8. maths

    find equations for the tangent and the normal at P (1n2, 2k) on the curve with equation y=ke^x, where k is a constant. (b) given that y=sin^-1x, show that (1-x^2)d^2y/dx^2-xdy/ dx=0

    asked by gibbsm on October 6, 2013
  9. maths

    find equations for the tangent and the normal at P (1n2, 2k) on the curve with equation y=ke^x, where k is a constant. (b) given that y=sin^-1x, show that (1-x^2)d^2y/dx^2-xdy/dx=0

    asked by skangele on October 3, 2013
  10. Differential Equation

    Verify whether the given equation (y=x^2+4x) is a solution to this given equation [(xdy/dx)=x^2+y]

    asked by Mycah on April 10, 2017

More Similar Questions