Which of the following is a homogeneous differential equation?
Which of the following is a homogeneous differential equation?
- A. dy/dx = (x+y)/x
- B. dy/dx = (x+y+1)/x
- C. dy/dx = x² + y
- D. dy/dx = sin(x) + y
Answer: A) dy/dx = (x+y)/x
Explanation: A differential equation dy/dx = f(x,y) is homogeneous if f(x,y) is a homogeneous function of degree zero. For (x+y)/x, replacing x,y with λx,λy gives (λx+λy)/λx = λ(x+y)/λx = (x+y)/x. The others fail this test.
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