The second order Lagerstrom ODE can be reduced to a first order ODE of Abel type once the system succeeds in finding one polynomial symmetry for it (see symgen):
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| (2) |
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| (3) |
From which, giving the same indication directly to dsolve, you obtain the reduction of order
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For the structure of the solution above see ODESolStruc. Reductions of order can also be tested with odetest
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The reduced ODE is of Abel type and can be selected using the mouse, or as follows
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| (6) |