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A homogeneous differential equation of the from can be solved by making the substitution.
Therefore, we shall substitute,
x = vy
In each of the question, show that the given differential equation is homogeneous and solve each of them.
(x2 + xy)dy = (x2 + y2)dx
(x – y)dy – (x + y)dx = 0
(x2 – y2)dx + 2xy dy = 0
For each of the differential equations in question, find the particular solution satisfying the given condition:
(x + y)dy + (x – y) dx = 0; y = 1 when x = 1
x2dy + (xy + y2)dx = 0; y = 1 when x = 1
y = 0 when x = 1