The solution of the differential equation dy = (1 + y²) dx is

Correct Answer is : y=tan⁡(x+c)y = (x + c)y=tan(x+c)

Correct Answer is : y=tan⁡(x+c)y = (x + c)y=tan(x+c)

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UPSC NDA I and II 2020 Math Solved Paper

Question : 67 of 120

Marks: +1, -0

dy = (1 + y^{2}) dx

Solution:

Concept:

The differential equation is separable. We integrate both sides after separating variables.

Explanation:

Step 1: Write the given equation:

dy = (1 + y^2) dx

Separate the variables:

\frac{dy}{1 + y^2} = dx

Step 2: Integrate both sides:

\int \frac{dy}{1 + y^2} = \int dx

The left integral gives

\tan^{-1} y

, the right gives

x + c

. Thus,

\tan^{-1} y = x + c

Step 3: Take tangent on both sides:

y = \tan(x + c)

This is the required solution.

Answer:

y = \tan (x + c)

(Option B).

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