Question

Form the differential equation corresponding to $y=cx-2c^2$ where c is a parameter.

Answer 1

$\begin{array}{c}y=cx-2c^2.......\left(i\right)\\ differentiatewithrespecttox\\ \frac{dy}{dx}=\frac{d\left(cx\right)}{dx}-\frac{d\left(2c^2\right)}{dx}\\ \frac{dy}{dx}=C-0\\ c=\frac{dy}{dx}.........\left(ii\right)\\ puttingc=\frac{dy}{dx}ine{q}^n..\left(i\right)\\ y=\frac{dy}{dx}\times x-2{\left(\frac{dy}{dx}\right)}^2\\ y=\frac{xdy}{dx}-2{\left(\frac{dy}{dx}\right)}^{2}itisrequireddiffentialequation\end{array}$