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Question
Form the differential equation of family of lines parallel to the line 2x + 3y + 4 = 0.
Solution
The equation of the line parallel to the line 2x + 3y + 4 = 0 is
2x + 3y + c = 0, where c is an arbitrary constant.
Differentiating w.r.t. x, we get
`2 xx 1 + 3 "dy"/"dx" 0 = 0`
`therefore 3 "dy"/"dx" + 2 = 0`
This is the required D.E.
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