(D) Given the differential equation: $(1 + x^2)\frac{dy}{dx} = 1$Separate the variables:$\frac{dy}{dx} = \frac{1}{1 + x^2}$$dy = \frac{1}{1 + x^2} dx$

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(D) Given the differential equation: $(1 + x^2)\frac{dy}{dx} = 1$Separate the variables:$\frac{dy}{dx} = \frac{1}{1 + x^2}$$dy = \frac{1}{1 + x^2} dx$Integrate both sides:$\int dy = \int \frac{1}{1 + x^2} dx$Using the standard integral formula $\int \frac{1}{1 + x^2} dx = \tan^{-1}x + c$,we get:$y = \tan^{-1}x + c$

Class 12 Mathematics Differential Equations Variable separable type differential equations

Easy

The solution of the equation $(1 + x^2)\frac{dy}{dx} = 1$ is

A
$y = \log(1 + x^2) + c$
B
$y + \log(1 + x^2) + c = 0$
C
$y - \log(1 + x) = c$
D
$y = \tan^{-1}x + c$

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The solution of the equation $(1 + x^2)\frac{dy}{dx} = 1$ is

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