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arroy_0205
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As far as I know, for an n-th order homogeneous linear differential equation, there are n number of linearly independent solutions and the general solution to the equation is a linear combination of them.
In the case of nth order homogeneous non-linear differential equation can it be shown that there are n number independent solutions? Can anybody tell me where I can find details of this? In case there are n number of independent solutions, I am not sure how to write the general solution. superposition principle will not hold. So what will be be the general solution? The degree of equation is one.
In the case of nth order homogeneous non-linear differential equation can it be shown that there are n number independent solutions? Can anybody tell me where I can find details of this? In case there are n number of independent solutions, I am not sure how to write the general solution. superposition principle will not hold. So what will be be the general solution? The degree of equation is one.
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