y^{'''}-y^{''}+y^'-y=xe^x-e^x+7

Lösung

y^{^{'''}} - y^{^{''}} + y^{^{'}} - y = x e^{x} - e^{x} + 7

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

Schritte zur Lösung

y^{'''} (x) - y^{''} (x) + y^{'} (x) - y = x e^{x} - e^{x} + 7

Solve linear ODE:

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

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

y^{^{''}} - 2 y^{^{'}} - 8 y = 2 sin (x) + (12 x - 10) e^{4 x}

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

y^{^{''}} + 16 y = - 8 sin (4 x) + 17 e^{x}

y^{^{''}} + 2 y^{^{'}} + 17 y = - 44 - 85 x

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