CUET Preparation Today
\(y=ex-c^{2}\) is the solution of the differential equation |
\(\left(\frac{dy}{dx}\right)^{2}+x\left(\frac{dy}{dx}\right)+y=0\) \(\frac{d^{2}y}{dx^{2}}=0\) \(\frac{dy}{dx}=0\) \(\left(\frac{dy}{dx}\right)^{2}-x\left(\frac{dy}{dx}\right)+y=0\) |
\(\left(\frac{dy}{dx}\right)^{2}-x\left(\frac{dy}{dx}\right)+y=0\) |
Check that \(y=ex-c^{2}\) satisfies the equation given in (d). \(\frac{dy}{dx}=c\hspace{1cm}\) So, \(\left(\frac{dy}{dx}\right)^{2}-x\left(\frac{dy}{dx}\right)+y=c^{2}-xc+cx-x^{2}=0\) |
