Question

The general solution of the differential equation y-xy' = x² + y² is

• A. y=xtanx+C
• B. y=tanx+C
• C. y=x²tanx+C
• D. y=xtan(C-x)
• E. y=xtanx+Cx

Answer 1

The Correct Option is A

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 \( y = x \tan(x) + C \).