y^{'''}+4y^{''}-5y=xe^x+8

Lösung

y^{^{'''}} + 4 y^{^{''}} - 5 y = x e^{x} + 8

y = c_{1} e^{x} + c_{2} e^{\frac{( - 5 + 5 ) x}{2}} + c_{3} e^{\frac{( - 5 - 5 ) x}{2}} + \frac{e ^{x} x ^{2}}{22} - \frac{7 e ^{x} x}{121} - \frac{8}{5}

Schritte zur Lösung

y^{'''} (x) + 4 y^{''} (x) - 5 y = x e^{x} + 8

Solve linear ODE:

y = c_{1} e^{x} + c_{2} e^{\frac{( - 5 + 5 ) x}{2}} + c_{3} e^{\frac{( - 5 - 5 ) x}{2}} + \frac{e ^{x} x ^{2}}{22} - \frac{7 e ^{x} x}{121} - \frac{8}{5}

y = c_{1} e^{x} + c_{2} e^{\frac{( - 5 + 5 ) x}{2}} + c_{3} e^{\frac{( - 5 - 5 ) x}{2}} + \frac{e ^{x} x ^{2}}{22} - \frac{7 e ^{x} x}{121} - \frac{8}{5}

y^{^{''}} - 12 y^{^{'}} + 36 y = e^{6 t} arctan (t)

y^{^{''}} + 2 y^{^{'}} - 3 y = 5 e^{2 x}, y (0) = 1, y^{^{'}} (0) = 0

y^{^{''}} + 3 y^{^{'}} - 4 y = 2, y (0) = 0, y^{^{'}} (0) = 0

y^{^{''}} + 3 y^{^{'}} - 4 y = 2, y (0) = 0, y^{^{'}} (0) = 1

\frac{d ^{2} y}{d x ^{2}} + 4 y = x - sin (3 x)