y^{''}+7y^'-12y=e^3x-2e^x-5x

Lösung

y^{^{''}} + 7 y^{^{'}} - 12 y = e^{3} x - 2 e^{x} - 5 x

y = c_{1} e^{\frac{( - 7 + 97 ) x}{2}} + c_{2} e^{\frac{( - 7 - 97 ) x}{2}} + \frac{- e ^{3} x + 5 x}{12} + \frac{1}{2} e^{x} + \frac{35 - 7 e ^{3}}{144}

Schritte zur Lösung

y^{''} (x) + 7 y^{'} (x) - 12 y = e^{3} x - 2 e^{x} - 5 x

Solve linear ODE:

y = c_{1} e^{\frac{( - 7 + 97 ) x}{2}} + c_{2} e^{\frac{( - 7 - 97 ) x}{2}} + \frac{- e ^{3} x + 5 x}{12} + \frac{1}{2} e^{x} + \frac{35 - 7 e ^{3}}{144}

y = c_{1} e^{\frac{( - 7 + 97 ) x}{2}} + c_{2} e^{\frac{( - 7 - 97 ) x}{2}} + \frac{- e ^{3} x + 5 x}{12} + \frac{1}{2} e^{x} + \frac{35 - 7 e ^{3}}{144}

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

\frac{d ^{2} y}{d x ^{2}} + 4 y = cos (\frac{9}{4} x)

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

y^{^{''}} + y = 2 sin (2) t

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