Question

If $y=2x+c$ is a solution of $y=x\frac{dy}{dx}+(\frac{dy}{dx}{)}^3-(\frac{dy}{dx}{)}^2+\left(\frac{dy}{dx}\right)$ then $c=$

Answer 1

Given that, $y=2x+c$ …… (1)

Differentiation this equation with respect to $x$ and we get,

$\frac{dy}{dx}=2\frac{dx}{dx}+0$

$\frac{dy}{dx}=2$

Put the given equation

$y=x\frac{dy}{dx}+{\left(\frac{dy}{dx}\right)}^3-{\left(\frac{dy}{dx}\right)}^2+\left(\frac{dy}{dx}\right)$

$y=2x+2^3-2^2+2$

$y=2x+6$ .….. (2)

Comparing equation (1) and (2) to, we get,

$c=6$

Hence, this is the answer.