- #1
BobMarly
- 19
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Find Solution 4*(x^2)*y"+y=0, y(-1)=2, y'(-1)=0
Not even sure where to start on this one?
Is this a series solution problem?
Not even sure where to start on this one?
Is this a series solution problem?
Last edited:
The solution to the differential equation 4*(x^2)*y + y = 0 is y = 2/x^4. This can be found by rearranging the equation and integrating both sides with respect to x.
To verify if a function is the solution to the differential equation, substitute the function into the equation and its derivatives. If the equation holds true, then the function is a valid solution.
The initial condition for this differential equation is y(-1) = 2, which means that when x = -1, y = 2.
To find the particular solution for this differential equation, substitute the given initial condition into the general solution and solve for the constant of integration. In this case, we have y = 2/x^4, and when x = -1, we get y = 2/(-1)^4 = 2.
The initial condition and derivative provide crucial information to find the particular solution for the differential equation. They serve as starting points and help determine the value of the constant of integration, which is essential in finding the specific solution.