Question

The differential equation of $y = ae^{bx}$ ($a \& b$ are parameters) is

• A. $yy_{1} = y^{2}_{2}$
• B. $yy_{2} = y^{2}_{1}$
• C. $yy_{1}^{2} = y_{2}$
• D. $yy_{2}^{2} = y_{1}$

Answer 1

Answer: (B)

Given, $y=a e^{b x}$
On differentiating w.r.t. $x$, we get
$y_{1}=a b e^{b x}$
$\Rightarrow y_{1}=b y$ ...(i)
Again differentiating, we get $y_{2}=b y_{1}$
$\Rightarrow y_{2}=\frac{y_{1}}{y} \cdot y_{1} $ [from Eq. (i)]
$\Rightarrow y_{1}^{2}=y y_{2}$