Find the general solution of: dy dx =y : - Vidyadip

MCQ

Find the general solution of$:\ \frac{\text{dy}}{\text{dx}}=\text{y}\sin\text{x:}$

A
$y + \log \sin x + c = 0$
B
$\log y - \cos x - c = 0$
✓
$\log y + \cos x - c = 0$
D
None of the above

✓

Answer

Correct option: C.

$\log y + \cos x - c = 0$

Concept:
$\int\frac{\text{dx}}{\text{x}}=\log\text{x}+\text{c}$
$\int\sin{\text{x}}{\text{ dx}}=-\cos\text{x}+\text{c}$
Calculation:
Given$:\ \frac{\text{dx}}{\text{dy}}=\text{y}\sin\text{x}$
$\Rightarrow\frac{\text{dx}}{\text{dy}}=\sin\text{x}\text{ dx}$
Integrating both sides, we get
$\Rightarrow\int\frac{\text{dy}}{\text{y}}=\int\sin\text{x}\text{ dx}$
$\Rightarrow\log\text{y}=-\cos\text{x}+\text{c}$
$\Rightarrow\log\text{y}+\cos\text{x}-\text{c}=0$

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