Question

The solutions of $y=x\left[\frac{dy}{dx}\right]+{\left[\frac{dy}{dx}\right]}^3$ are given by (where p = dy/dx and k is constant)

• A. y = 0
• B. $y=kx+k^3$
• C. $y=k{e}^{x+k}$
• D. none of these

Answer 1

The correct option is A y = 0

Let $\frac{dy}{dx}=P$

$y=xP+P^3$

diff. both side $w.r.t.x$

$\frac{dy}{dx}=P+3P^2\frac{dP}{dx}$

$P=P+3P^2\frac{dP}{dx}$

$\frac{dP}{dx}=0$

integrate both side,

$P=0$ , $\frac{dy}{dx}=0$ , $y=0$.