Question

The differential equation obtained by eliminating $a$ and $b$ from $y=a{e}^{bx}$ is

• A. $yy"={\left(y^{\prime }\right)}^2$
• B. $yy"=y^{\prime }$
• C. $y{y}^{\prime }={(y")}^2$
• D. $y"={\left(y^{\prime }\right)}^2$

Answer 1

The correct option is A $yy"={\left(y^{\prime }\right)}^2$

$y=a{e}^{bx}$

$\Rightarrow y_1=ab{e}^{bx}$

$\Rightarrow y_2=a{b}^2{e}^{bx}$

We can see that,

$y{y}_2=(y_1{)}^2$

or $y{y}^{\prime \prime }=(y^{{}^{\prime }}{)}^2$