y^{''}-8y^'+20y=100x^2-65

Lösung

y^{^{''}} - 8 y^{^{'}} + 20 y = 100 x^{2} - 65

y = e^{4 x} (c_{1} cos (2 x) + c_{2} sin (2 x)) + 5 x^{2} + 4 x - \frac{43}{20}

Schritte zur Lösung

y^{''} (x) - 8 y^{'} (x) + 20 y = 100 x^{2} - 65

Solve linear ODE:

y = e^{4 x} (c_{1} cos (2 x) + c_{2} sin (2 x)) + 5 x^{2} + 4 x - \frac{43}{20}

y = e^{4 x} (c_{1} cos (2 x) + c_{2} sin (2 x)) + 5 x^{2} + 4 x - \frac{43}{20}

y^{^{''}} + 2 y^{^{'}} - 8 y = 4 e^{- 2 x} - e^{- x}

y^{^{''}} - 4 y^{^{'}} + 4 y = (x + 1) \cdot e^{2 x}

y^{^{''}} + 6 y^{^{'}} + 13 y = 10 e^{- 2 t}, y (0) = 3

4 y^{^{''}} + y = sin (t), y (0) = 0, y^{^{'}} (0) = 1

y^{^{'''}} + 289 y^{^{'}} = tan (17 x)