y^{''}-2y^'-3y=2xe^{3x}

Lösung

y^{^{''}} - 2 y^{^{'}} - 3 y = 2 x e^{3 x}

y = c_{1} e^{3 x} + c_{2} e^{- x} + \frac{e ^{3 x} x ^{2}}{4} - \frac{e ^{3 x} x}{8}

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} e^{- x} + \frac{e ^{3 x} x ^{2}}{4} - \frac{e ^{3 x} x}{8}

y = c_{1} e^{3 x} + c_{2} e^{- x} + \frac{e ^{3 x} x ^{2}}{4} - \frac{e ^{3 x} x}{8}

y^{^{''}} - 2 y^{^{'}} = 8 x

0.5 y^{^{''}} + 6 y^{^{'}} + 50 y = 240 cos (10 t)

y^{^{''}} + y = 4 \cdot cos (x)

y^{^{''''}} - y = 8 t + cos (t)

y^{^{''}} + 2 y^{^{'}} = x^{2}