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Solve (x+y-1)dy-(x-y+2)dx=0

Solve (x+y−1)dy−(x−y+2)dx=0 (x+y-1) d y-(x-y+2) d x=0

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Q. Solve (x+y−1)dy−(x−y+2)dx=0 (x+y-1) d y-(x-y+2) d x=0
  1. Divide and Calculate: First, we need to divide the total amount of tape needed by the amount of tape on each roll.\newlineSo, we do 8,000 cm÷2,000 cm.8,000 \, \text{cm} \div 2,000 \, \text{cm}.
  2. Order Rolls of Tape: Calculating 8,000÷2,0008,000 \div 2,000 gives us 44.\newlineSo, the electrician needs to order 44 rolls of tape.
  3. Rearrange and Group: We can start by rearranging the terms to group dxdx and dydy on one side.\newlineSo, we get (x+y−1)dy=(x−y+2)dx(x+y-1)dy = (x-y+2)dx.
  4. Integrate Both Sides: Now, we integrate both sides of the equation. Integrating (x+y−1) dy(x+y-1)\,dy on the left side and (x−y+2) dx(x-y+2)\,dx on the right side.
  5. Calculate Integral: The integral of (x+y−1)dy(x+y-1)dy is x∗y+12y2−y+C1x*y + \frac{1}{2}y^2 - y + C_1, where C1C_1 is the constant of integration.

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