Differential EquationHard
Question
The equation of the curve which is such that the portion of the axis of x cut off between the origin and tangent at any point is proportional to the ordinate of that point is
Options
A.x = y (b - a log y)
B.log x = by2 + a
C.x2 = y (a - b log y)
D.none of these
Solution
Y - y = m(x - x)
Xint =
+ x = ay
= ay - x ⇒ m = 
⇒ 
- = - a
I.F. = e∫1/y dy =
x .
= - a 
by
= - a logy + b
x = y(b - a log y)
Xint =
+ x = ay= ay - x ⇒ m = ⇒ - = - a I.F. = e∫1/y dy =
x .
= - a by = - a logy + bx = y(b - a log y)
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