Solve (4xy+3y^2–x)dx+x(x+2y)dy=0

Solve (4xy+3y^2–x)dx+x(x+2y)dy=0

Problem

Solution

Problem

Solve (4xy+3y^2–x)dx+x(x+2y)dy=0

Topic

Exact differential equations

Type 1 Questions

  1. Solve dy/dx+(x+3y-4)/(3x+9y-2)=0
  2. Solve dy/dx+(y cosx +siny +y)/(sinx + xcosy +x)=0
  3. Solve ye^xy dx+(xe^xy +2y)dy=0
  4. Solve (1+e^(x/y))dx+e^(x/y) (1-x/y)dy=0
  5. Solve (y^2 e^(xy^2) + 4x^3)dx+(2xy e^(xy^2)-3y^2)dy=0
  6. Solve 2x/y^3 dx+(y^2-3x^2/y^4) dy=0

 

Type 2 Questions

  1. Solve (4xy+3y^2–x)dx+x(x+2y)dy=0
  2. Solve (x^2+y^2+x)dx+xydy=0
  3. Solve y(2xy+1)dx–xdy=0
  4. Solve (2xlogx–xy)dy + 2ydx = 0

This Post Has 2 Comments

  1. Anurag Rana March 8, 2024 Reply

    in last while solution it should not be integration of 0dy it shoukd be 2x^3y bcoz it also contain y not x alone it should be their and integrate

    1. admin March 10, 2024 Reply

      Hi Anurag
      Thanks for visiting! Your response is much appreciated. The Solution to the problem is correct. N(y) indicates the terms in ‘N’ without ‘x'(not containing ‘x’). In N = x^4 +2x^3y there is no term without ‘x’, hence N(y) is taken as 0. Hope this will be helpful.

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