Question:
The solution of the differential equation
\[
\frac{dy}{dx}=1+y^2
\]
is
The solution of the differential equation
\[
\frac{dy}{dx}=1+y^2
\]
is
Show Hint
Remember \(\int\frac{dy}{1+y^2}=\tan^{-1}y\).
Updated On: May 27, 2026
- \(y=\tan x+c\)
- \(y=\tan(x+c)\)
- \(y=\tan x\)
- \(y=-\tan(x+c)\)
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The Correct Option is B
Solution and Explanation
Step 1: Given: \[ \frac{dy}{dx}=1+y^2 \]
Step 2: Separate variables: \[ \frac{dy}{1+y^2}=dx \]
Step 3: Integrate both sides: \[ \int\frac{dy}{1+y^2}=\int dx \] \[ \tan^{-1}y=x+c \]
Step 4: Taking tangent both sides: \[ y=\tan(x+c) \] \[ \boxed{y=\tan(x+c)} \]
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