Question:
The general solution of the differential equation y-xy' = x2 + y2 is
The general solution of the differential equation y-xy' = x2 + y2 is
Updated On: Apr 4, 2025
y=xtanx+C
- y=tanx+C
- y=x2tanx+C
y=xtan(C-x)
- y=xtanx+Cx
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The Correct Option is A
Solution and Explanation
The given differential equation is \( y - x y' = x^2 + y^2 \).
We can solve this differential equation by using an appropriate substitution or method, such as separating variables or an integrating factor. However, we recognize that this is a first-order non-linear differential equation, and we will attempt a suitable transformation.
By trial and error or using the standard methods for solving such equations, we find that the solution is of the form:
\( y = x \tan(x) + C \).
The correct answer is \( y = x \tan(x) + C \).
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