(D^4-1)y=7x^2

Lösung

(D^{4} - 1) y = 7 x^{2}

y = c_{1} e^{x} + c_{2} e^{- x} + c_{3} cos (x) + c_{4} sin (x) - 7 x^{2}

Schritte zur Lösung

(D^{4} - 1) y = 7 x^{2}

Solve linear ODE:

y = c_{1} e^{x} + c_{2} e^{- x} + c_{3} cos (x) + c_{4} sin (x) - 7 x^{2}

y = c_{1} e^{x} + c_{2} e^{- x} + c_{3} cos (x) + c_{4} sin (x) - 7 x^{2}

y^{^{''}} - 2 y^{^{'}} - 3 y = 4 e^{5 x}

y^{^{'''}} - y = 1

y^{^{''}} + 7 y^{^{'}} + 12 y = 4 e^{5 t}, y (0) = 2, y^{^{'}} (0) = 0

y^{^{''}} - 2 y^{^{'}} - 8 y = 2 e^{4 x} + 3 x e^{2 x} + 4 x

\frac{d ^{2} y}{d t ^{2}} - 2 \frac{d y}{d t} - 15 y = 6 + 4 t