y^{'''}=3y^{''}+9e^3x+5cos(x)

Lösung

y^{^{'''}} = 3 y^{^{''}} + 9 e^{3} x + 5 cos (x)

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

Schritte zur Lösung

y^{'''} (x) = 3 y^{''} (x) + 9 e^{3} x + 5 cos (x)

Solve linear ODE:

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

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

y^{^{''}} + 9 y = 10 e^{-} 1, y (0) = 0, y^{^{'}} (0) = 0

y^{^{''}} + 4 y^{^{'}} - 5 y = 24 e^{x}

y^{^{''}} - 4 y^{^{'}} + 4 y = e^{2 x} sin (x)

y^{^{''}} + 2 y^{^{'}} - 3 y = e^{- 3 t}

\frac{d ^{2} y}{d x ^{2}} - a^{2} y + b = 0