Q2 Which of the following differential equations are homogeneous?

1. (x - y)
   dy / dx
   =x+2y
2. y-x
   dy / dx
   =x+y
   dy / dx
3. (x² + 3xy - 4y²) dx - x (x² + 2y) dy = 0
4. x
   dy / dx
   +y=xtan^-1
   y / x
5. x cos(
   y / x
   )
   dy / dx
   =y cos (
   y / x
   ) -3x²
6. x
   dy / dx
   -y=√x² +y²
7. (x² +y²sin
   x / y
   )
   dy / dx
   =2xy e^x/y
8. 2y e^1/y dx + (y-2x e^1/y ) dy=0
9. ydx +xlog (
   y / x
   )dy-2x dy=0

Solution

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