Question

The differential equation corresponding to primitive $y=e^{dx}$ is

or

The elimination of the arbitrary constant m from the equation $y=e^{mx}$ gives the differential equation

[MP PET 1995, 2000; Pb. CET 2000]

• A. $\frac{dy}{dx}=\left(\frac{y}{x}\right)logx$
• B. $\frac{dy}{dx}=\left(\frac{x}{y}\right)logy$
• C. $\frac{dy}{dx}=\left(\frac{y}{x}\right)logy$
• D. $\frac{dy}{dx}=\left(\frac{x}{y}\right)logx$

Answer 1

The correct option is C

$\frac{dy}{dx}=\left(\frac{y}{x}\right)logy$

$y=e^{mx}\Rightarrow logymx\Rightarrow m=\frac{logy}{x}y=e^{mx}\Rightarrow \frac{dy}{dx}=m{e}^{mx}=\frac{logy}{x}y=\left(\frac{y}{x}\right)logy.$