What is the solution of the differential equation: In ( dx dy )-a… - Vidyadip

MCQ

What is the solution of the differential equation$:\ \text{In}\Big(\frac{\text{dx}}{\text{dy}}\Big)-\text{a}=0?$

✓
$y=x e^a+c$
B
$x=y e^a+c$
C
$\text{y = In x + c}$
D
$\text{x = In y + c}$

✓

Answer

Correct option: A.

$y=x e^a+c$

Calculation:
Given: $\text{In}\Big(\frac{\text{dy}}{\text{dx}}\Big)-\text{a}=0$
$\Rightarrow\text{In}\Big(\frac{\text{dy}}{\text{dx}}\Big)=\text{a}$
$\Rightarrow\frac{\text{dy}}{\text{dx}}=\text{e}^\text{a}$
$\Rightarrow\int\frac{\text{dy}}{\text{dx}}=\int\text{e}^\text{a}$
On integrating both sides, we get
$\Rightarrow\text{y}=\text{xe}^\text{a}+\text{c}$

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