The differential equation of y = aebx (a b are parameters) is

Question

The differential equation of y = aebx (a b are parameters) is (A) yy1 = y22 (B) yy2 = y21 (C) yy12 = y2 (D) yy22 = y1

Tardigrade Admin · Accepted Answer

Given, y=a eb x On differentiating w.r.t. x, we get y1=a b eb x ⇒ y1=b y ...(i) Again differentiating, we get y2=b y1 ⇒ y2=(y1/y) ⋅ y1 [from Eq. (i)] ⇒ y12=y y2

Q. The differential equation of $y = a e^{b x}$ ( $a & b$ are parameters) is

$y y_{1} = y_{2}^{2}$

$y y_{2} = y_{1}^{2}$

$y y_{1}^{2} = y_{2}$

$y y_{2}^{2} = y_{1}$

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

Q. The differential equation of y=aebx (a&b are parameters) is

yy1​=y22​

yy2​=y12​

yy12​=y2​

yy22​=y1​