16 нояб. 2022 г. · In this section we will be looking at the last case for the constant coefficient, linear, homogeneous second order differential equations. |
Two distinct real roots: b2 - 4ac > 0. ( r1 ≠ r2 ) ii.A repeated real root: b2 - 4ac = 0. iii.Two complex roots: b2 - ... |
This is demonstrated with an example. Example \(\PageIndex{3}\). Given that \(y_1 = t\) is a solution to the differential equation. Example \(\PageIndex{1... · Example \(\PageIndex{2}\) |
Example 1. Solve the differential equation y00 + 4y0 + 4y = 0. Solution. The characteristic equation is r2 + 4r +4=(r + 2)2 = 0, so r = −2 is a double root. |
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