Question:
The solution of the differential equation
\[
\frac{dy}{dx} = (4x + y + 1)^2
\]
is:
The solution of the differential equation
\[
\frac{dy}{dx} = (4x + y + 1)^2
\]
is:
Show Hint
To solve differential equations with separable variables, separate the terms and integrate both sides.
Updated On: Jan 6, 2026
- \( (4x + y + 1) = \tan(2x + C) \)
- \( (4x + y + 1) = 2 \tan(2x + C) \)
- \( (4x + y + 1) = 3 \tan(2x + C) \)
- \( (4x + y + 1) = 2 \tan(2x + C) \)
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The Correct Option is D
Solution and Explanation
Step 1: Separate variables and integrate.
We integrate the equation to find the general solution. The result will match the form \( (4x + y + 1) = 2 \tan(2x + C) \).
Step 2: Conclusion.
Thus, the correct solution is \( (4x + y + 1) = 2 \tan(2x + C) \).
Final Answer: \[ \boxed{2 \tan(2x + C)} \]
We integrate the equation to find the general solution. The result will match the form \( (4x + y + 1) = 2 \tan(2x + C) \).
Step 2: Conclusion.
Thus, the correct solution is \( (4x + y + 1) = 2 \tan(2x + C) \).
Final Answer: \[ \boxed{2 \tan(2x + C)} \]
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