Find the general solution for x^2*y''-2y=0

In summary, the conversation discusses the difficulty in finding a clear solution for the equation x^2*y''-2y=0 using the desolve function, as well as the challenges in correctly formatting the input. It is advised to consult the manual for proper manipulation of the equation.
  • #1
Octavius1287
30
0
I have searched for a long time and i can't find a clear answer

I want to find the general solution for x^2*y''-2y=0 using deslove and i typed it in as

desolve(x^2*y''-2y=0,y) and it says too few arguments
then i tried
desolve(x^2*y''-2y=0,y,x) same thing, then i switched the y ans the x didnt help

And i can't find any where the right format to use to solve this
 
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  • #2
In cases like these, one must consult the manual.

Calculators and computers are notoriously balky about accepting any old input.
For your equation, you must manipulate it so that it becomes y'' = stuff.
 

1. What is the general solution for x^2*y''-2y=0?

The general solution for this differential equation is y = C1*x^2 + C2/x, where C1 and C2 are arbitrary constants.

2. How do you derive the general solution for this equation?

To derive the general solution, we can use the method of undetermined coefficients. We assume a solution of the form y = Ax^2 + B/x, where A and B are constants, and plug this into the original equation. We then solve for A and B to get the general solution.

3. What is the significance of the arbitrary constants in the general solution?

The arbitrary constants represent the infinite number of solutions to the given differential equation. They allow us to account for all possible values of y that satisfy the equation.

4. Can the general solution be used to find a particular solution?

Yes, the general solution can be used to find a particular solution by substituting specific values for the arbitrary constants. This will give a specific solution that satisfies the equation.

5. Are there any other methods to solve this type of differential equation?

Yes, there are other methods such as the method of variation of parameters and the method of reduction of order that can also be used to find the general solution for this type of differential equation.

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