Find a particular solution of the non-homogeneous system of…
Find a particular solution of the non-homogeneous system of differential equations \[ X’ = \left[ \begin{array}{ll} 2 & 3 \\ 1 & 4 \end{array} \right]X + \left[ \begin{array}{r} 3e^{2t} \\ 0 \end{array} \right] + \left[ \begin{array}{r} 0 \\ 5 \end{array} \right] \]
Read DetailsTo analyze a nonlinear differential equation, y ″ + si…
To analyze a nonlinear differential equation, y ″ + sin ( y ) = 0 , {“version”:”1.1″,”math”:”\(\, y” + \sin(y) \, = \, 0, \, \)”}we set up a system of first order differential equations by letting y 1 = y {“version”:”1.1″,”math”:”\(\, y_1 = y\, \)”}and y 2 = y ′ . {“version”:”1.1″,”math”:”\(\, y_2 = y’. \)”} y 1 ′ = y 2 y 2 ′ = − sin ( y 1 ) . {“version”:”1.1″,”math”:”\begin{eqnarray*} y’_1 \ = \ y_2 \qquad\qquad y’_2 \ = \ – \sin(y_1). \end{eqnarray*}”}When we use the linearization to classify the system’s critical points, find the statement which is WRONG for the linearization?
Read DetailsIf the linear system ( x + 2 y + 4 z = 3 3 x +…
If the linear system ( x + 2 y + 4 z = 3 3 x + 5 y + 2 = 4 − x − y + k z = 2 {“version”:”1.1″,”math”:” \left( \begin{array}{lll} x + 2y + 4z & = & 3 \\ 3x + 5y + 2 & = & 4 \\ -x – y + kz & = & 2 \\ \end{array} \right.”}has infinitely many solutions, then which number is the value of k {“version”:”1.1″,”math”:”\(\, k\)”}?
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