Question

Consider the differential equation dy/dx = -2x/y. What is the general solution?

A) y = e(ˣ²)
B) y = x²
C) y = -x²
D) y = e(⁻ˣ²)

Answer 1

The general solution to the differential equation dy/dx = -2x/y is y = ±√(2(-x^2 + C)), where C is any constant.

Step-by-step explanation:

To solve the differential equation dy/dx = -2x/y, we can separate the variables. Multiply both sides by y to get -2x dy = y dx. Now, integrate both sides with respect to x: ∫-2x dy = ∫y dx. This gives us -x^2 + C = y^2/2, where C is the constant of integration.

To find the general solution, we can rearrange the equation to isolate y: y^2 = 2(-x^2 + C). Taking the square root of both sides, we have y = ±√(2(-x^2 + C)). So the general solution is y = ±√(2(-x^2 + C)), where C is any constant.