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BobMarly
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General Solution for (x^2)*y"+x*y'-y=1/(x+1)
Where do I start?
Where do I start?
A general solution is a mathematical expression that satisfies a given equation or set of equations. It includes all possible solutions to the equation, rather than a specific or unique solution.
To find the general solution, you can use a method called separation of variables. First, rearrange the equation to have all the y terms on one side and all the x terms on the other side. Then, integrate both sides with respect to x. This will give you the general solution in the form of a function.
The "y' " term represents the derivative of the function y with respect to x. It is also known as the slope of the function at a given point.
You can plug in the values of x and y from the particular solution into the general solution equation. If the resulting expression is equal to the right side of the original equation, then the particular solution is a valid solution within the general solution.
Yes, there may be restrictions depending on the specific equation. In the case of (x^2)*y +x*y'-y=1/(x+1), the value of x cannot be equal to -1, as this would result in division by zero. Additionally, the general solution may only be applicable for certain ranges of values for x and y, which can be determined by analyzing the equation.