y^{''}-2y^'+2y=ex,y(pi/2)=0,y(0)=0

Lösung

y^{^{''}} - 2 y^{^{'}} + 2 y = e x, y (\frac{π}{2}) = 0, y (0) = 0

y = e^{x} (- \frac{e}{2} cos (x) + \frac{- π e - 2 e}{4 e ^{\frac{π}{2}}} sin (x)) + \frac{e x}{2} + \frac{e}{2}

Schritte zur Lösung

y^{''} (x) - 2 y^{'} (x) + 2 y = e x

Solve linear ODE:

y = e^{x} (- \frac{e}{2} cos (x) + \frac{- π e - 2 e}{4 e ^{\frac{π}{2}}} sin (x)) + \frac{e x}{2} + \frac{e}{2}

y = e^{x} (- \frac{e}{2} cos (x) + \frac{- π e - 2 e}{4 e ^{\frac{π}{2}}} sin (x)) + \frac{e x}{2} + \frac{e}{2}

x^{^{''}} + 4 x^{^{'}} + 20 x = 4 cos (2 t)

y^{^{''}} + y^{^{'}} - 6 y = - 5 e^{- 2 x}

y^{^{''}} + y = 3 cos (4 t), y (0) = 1, y^{^{'}} (0) = 2

x^{^{''}} + x = \frac{1}{cos ( t )}

y^{^{''}} - 6 y^{^{'}} + 10 y = e^{3 x} cos (x)