The solution of the differential equation dy = (1 + y^2) dx is : - Vidyadip

MCQ

The solution of the differential equation $dy = (1 + y^2) dx$ is :

A
$\text{y}=\tan\text{x}+\text{c}$
✓
$\text{y}=\tan(\text{x}+\text{c})$
C
$\tan^{-1}(\text{y}+\text{c})=\text{x}$
D
$(\tan^{-1}(\text{y}+\text{c})=2\text{x}$

✓

Answer

Correct option: B.

$\text{y}=\tan(\text{x}+\text{c})$

Given : $dy = (1 + y^2) dx$
$\Rightarrow\frac{\text{dy}}{1+\text{y}^2}\text{dx}$
Integrating both sides, we get
$\Rightarrow\int\frac{\text{dy}}{1+\text{y}^2}=\int\text{dx}$
$\Rightarrow\tan^{-1}\text{y}=\text{x}+\text{c}$
$\Rightarrow\text{y}=\tan(\text{x}+\text{c})$

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