Question

An equation of the curve in which subnormal varies as the square of the ordinate is (k is constant of proportionality)

• A. $y=A{e}^{kx}$
• B. $y=e^{kx}$
• C. $\frac{y^2}{2}+kx=A$
• D. $y^2+k{x}^2=A$

Answer 1

The correct option is A $y=A{e}^{kx}$

According to the given condition $y\frac{dy}{dx}=k{y}^2$
$\Rightarrow \frac{dy}{y}=kdx$(variables separable equation)
$\Rightarrow log|y|=kx+C\Rightarrow |y|=B{e}^{kx}$
​$\Rightarrow y=A{e}^{kx}$ where $A=\pm B$ and k is the constant of proportionality.