y^{''}+3y^'-10y=e^{(2x)}+xe^{(-5x)}

Lösung

y^{^{''}} + 3 y^{^{'}} - 10 y = e^{(2 x)} + x e^{(- 5 x)}

y = c_{1} e^{2 x} + c_{2} e^{- 5 x} + \frac{e ^{2 x} x}{7} - \frac{e ^{- 5 x} x ^{2}}{14} - \frac{e ^{- 5 x} x}{49}

Schritte zur Lösung

y^{''} (x) + 3 y^{'} (x) - 10 y = e^{(2 x)} + x e^{(- 5 x)}

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} e^{- 5 x} + \frac{e ^{2 x} x}{7} - \frac{e ^{- 5 x} x ^{2}}{14} - \frac{e ^{- 5 x} x}{49}

y = c_{1} e^{2 x} + c_{2} e^{- 5 x} + \frac{e ^{2 x} x}{7} - \frac{e ^{- 5 x} x ^{2}}{14} - \frac{e ^{- 5 x} x}{49}

y^{^{''}} + y - 7 x sin (x) = 0

x^{^{''}} + 2 x^{^{'}} + x = e^{2 t}, x (0) = 2, x^{^{'}} (0) = 1

y^{^{''}} + 2 y^{^{'}} + 5 y = 0, y (0) = 0, y^{^{'}} (0) = - 2

16 \frac{d ^{4} y}{d x ^{4}} + 24 \frac{d ^{2} y}{d x ^{2}} + 9 y = 0

y^{^{''}} + 2 y^{^{'}} + y = 0, y (0) = 1, y^{^{'}} (0) = 1