Ordinary Differential Equations/Non Homogenous 4: Difference between revisions

Latest revision as of 20:25, 22 May 2019

1. $y^{″} - y = e^{- x}, x \in ℝ, y (0) = y^{'} (0) = 0$

Answer: $y (x) = \frac{1}{4} e^{x} - \frac{1}{4} e^{- x} - \frac{1}{2} x e^{- x}$

1. $y^{″} - 7 y + 12 y = 24 e^{x}$

Answer: $y_{p} (x) = 4 e^{- x}$

2. $y^{″} + 4 y^{'} + 4 y = e^{- 2 x}$

Answer: $y_{p} (x) = \frac{1}{2} x^{2} e^{- 2 x}$