17.3k views
1 vote
The general solution of x²y′ + 2y = 2e¹/ˣ√y is:

User Zaneta
by
8.9k points

1 Answer

5 votes

Final answer:

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.

User Oblomov
by
8.7k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.