Question
Form the differential equation of $y = (c_1 + c_2)e^x$
✓
Answer
$ y=\left(c_1+c_2\right) e^x$
$=A e^x, \quad \ldots(i) $
Where $A=\left(c_1+c_2\right)$
Here, A is an arbitrary constant.
Differentiating (i) w.r.t. x, we get
$ \frac{ d y}{ d x}= Ae ^{ x }$
$\therefore \frac{ d y}{d x}= y \quad \ldots . .[\text { From (i)] } $
$=A e^x, \quad \ldots(i) $
Where $A=\left(c_1+c_2\right)$
Here, A is an arbitrary constant.
Differentiating (i) w.r.t. x, we get
$ \frac{ d y}{ d x}= Ae ^{ x }$
$\therefore \frac{ d y}{d x}= y \quad \ldots . .[\text { From (i)] } $
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