Differential equation whose solution is y = cx + c - c^3 , is - Vidyadip

MCQ

Differential equation whose solution is $y = cx + c - {c^3}$, is

A
$\frac{{dy}}{{dx}} = c$
✓
$y = x\frac{{dy}}{{dx}} + \frac{{dy}}{{dx}} - {\left( {\frac{{dy}}{{dx}}} \right)^3}$
C
$\frac{{dy}}{{dx}} = c - 3{c^2}$
D
None of these

✓

Answer

Correct option: B.

$y = x\frac{{dy}}{{dx}} + \frac{{dy}}{{dx}} - {\left( {\frac{{dy}}{{dx}}} \right)^3}$

b
(b) Differentiating, we have $\frac{{dy}}{{dx}} = c$

Hence differential equation is, $y = x\frac{{dy}}{{dx}} + \frac{{dy}}{{dx}} - {\left( {\frac{{dy}}{{dx}}} \right)^3}$.

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