Question

solve (x+y-2)dx+(x-y+4)dy=0

Answer 1

x²/2 - y²/2 + xy - 2x + 4y = C

Step-by-step explanation:

The given differential equation is

(x + y - 2) dx + (x - y + 4) dy = 0

or, x dx + y dx - 2 dx + x dy - y dy + 4 dy = 0

or, x dx - y dy + (x dy + y dx) - 2 dx + 4 dy = 0

or, x dx - y dy + d(xy) - 2 dx + 4 dy = 0

Integrating on both sides, we get

x²/2 - y²/2 + xy - 2x + 4y = C

where C is the constant of integration

This is the required solution.

Solve these problems at home:

1. (y + x) dx + x dy = 0

2. y dx - x dy + logx dx = 0

3. (1 + xy)y dx + (1 - xy)x dy = 0

4. (x + y) dy + (y - x) dx = 0

5. x dx + y dy = k (x dy - y dx)