Example Sentences

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If we are able to find two linearly independent solutions to a second-order differential equation, then we can combine them to find the general solution.

From Textbooks • Mar. 30, 2016

Using some smart choices for c1 and c2, and a little bit of algebraic manipulation, we can find two linearly independent, real-value solutions to Equation 7.1 and express our general solution in those terms.

From Textbooks • Mar. 30, 2016

Note that y1 and y2 are not constant multiples of one another, so they are linearly independent.

From Textbooks • Mar. 30, 2016

If we can find two linearly independent solutions to a differential equation, we have, effectively, found all solutions to the differential equation—quite a remarkable statement.

From Textbooks • Mar. 30, 2016

When exactly r of them are linearly independent, the self-conjugate group generated by them coincides with the original group.

From Encyclopaedia Britannica, 11th Edition, Volume 12, Slice 6 "Groups, Theory of" to "Gwyniad" by Various