Question

The differential equation of $y = e^{bx}$ (a and b are parameter) is

• A. $ y y_1 = y^2_2$
• B. $y y^2 = y^2_1$
• C. $y y^2_1 = y_2$
• D. $y y^2_2 = y_1$

Answer 1

Answer: (B)

$y = e^{bx}$
$\Rightarrow y_{1} = ba\,e^{bx}$
$\Rightarrow y_{2} = ab^{2}\,e^{bx}$
$\therefore y^{2}_{1} = a^{2}\,b^{2}\,e^{2bx}$
$= \left(a \,e^{bx}\right) \left(ab^{2}\, e^{bx}\right) = y\, y_{2}$
$\therefore y\,y_{2} = y^{2}_{1}$.