What is the solution of the differential equation dy dx + y x =0?… - Vidyadip

MCQ

What is the solution of the differential equation $\frac{\text{dy}}{\text{dx}}+\frac{\text{y}}{\text{x}}=0?$ Where c is a constant.

✓
xy = c
B
x = cy
C
y = cx
D
None of the above

✓

Answer

Correct option: A.

xy = c

Givenexpression is

$\frac{\text{dy}}{\text{dx}}+\frac{\text{y}}{\text{x}}=0$

$\Rightarrow\frac{\text{dy}}{\text{dx}}=-\frac{\text{y}}{\text{x}}$

$\Rightarrow\frac{\text{dy}}{\text{y}}=-\frac{\text{dx}}{\text{x}}=0$

Integrating we get

$\int\frac{\text{dy}}{\text{y}}+\frac{\text{dx}}{\text{x}}=0$

$\Rightarrow\text{In}\text{ y}+\text{In}\text{ x}=\text{c}$

$\Rightarrow\text{x}{\text{y}}=\text{c}$

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