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Find a real general solution. Show the details of your work. xy''+2y'=0
into the given ODE. This gives:
Multiply the equation by :
We can see that is a common factor, dropping it gives:
So, is a solution of the given ODE if is a root of the equation
Let's find the roots of the equation .
So, it has the distinct real roots:
Real different roots and provide two real solutions:
Their quotient is not constant, so the solutions and are linearly independent and constitute a basis of solutions for the given ODE, for all x for which .
So, the general solution is:
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