Question

The general solution of x²y′ + 2y = 2e¹/ˣ√y is:

Answer 1

To find the general solution of the given differential equation, use the method of separation of variables and integrate both sides.

Step-by-step explanation:

The general solution of the differential equation x²y′ + 2y = 2e^(1/(x√y)) can be found using the method of separation of variables and integrating both sides of the equation. Here are the steps:

1. Divide both sides of the equation by x² to get y′ + (2/x²)y = 2e^(1/(x√y))/x².
2. Rewrite the equation as 1/y dy = -2/x² dx + 2e^(1/(x√y))/x² dx.
3. Integrate both sides of the equation with respect to their respective variables.
4. Solve for y to obtain the general solution.

I hope this helps! Let me know if you have any further questions.