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The solution of the differential equation (1+y²)+(x-e^(tan⁻¹y)) dy/dx=0, is
- x e^(2tan⁻¹y)=e^(tan⁻¹y)+k
- (x-2)=k e^(2tan⁻¹y)
- 2x e^(tan⁻¹y)=e^(2tan⁻¹y)+k
- x e^(tan⁻¹y)=tan⁻¹y+k
Correct answer: 2x e^(tan⁻¹y)=e^(2tan⁻¹y)+k
Solution
The correct option is derived from solving the given differential equation using an appropriate method, such as separation of variables or integrating factors, leading to a relationship that correctly represents the solution in terms of the variables involved.
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