question_answer 77)

Which of the following is a homogeneous differential equation ? (a) (4x + 6y + 5) dy – (3y + 2x + 4) dx = 0 (b) xy dx – (x3 + y3) dy = 0 (c) (x3 + 2y2) dx + 2xy dy = 0 (d) y2 dx + (x2 – xy – y2) dy = 0  

Answer:

y2dx + (x2 ? xy ? y2) dy = 0 can be written as .       Divide numerator and denominator by x2             Clearly it is homogeneous differential equation of degree 0.        is correct.