Question

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

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

Answer 1

Answer: (B)

$y=e^{bx}$
$\Rightarrow y_1=ba{e}^{bx}$
$\Rightarrow y_2=a{b}^2{e}^{bx}$
$\therefore y_1^2=a^2{b}^2{e}^{2bx}$
$=\left(a{e}^{bx}\right)\left(a{b}^2{e}^{bx}\right)=y{y}_2$
$\therefore y{y}_2=y_1^2$.