A third order nonlinear ODE
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No general solution is known for ode. A particular solution for it, however, depending on one arbitrary constant, is computable via
A second order non-homogeneous linear ODE whose homogeneous part is out of the scope of dsolve and a particular rational solution for it
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Represent this non-homogeneous linear ODE using a list with the coefficients of y(x) and its derivatives
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Note particularsol is not restricted to the computation of rational particular solutions
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