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

Lösung

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

y = c_{1} + c_{2} e^{- 2 x} + c_{3} e^{2 x} + \frac{- 160 x ^{3} + 120 e ^{2 x} x ^{2} - 180 e ^{2 x} x - 240 x + 105 e ^{2 x} + 384 cos ( x )}{1920}

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} + c_{2} e^{- 2 x} + c_{3} e^{2 x} + \frac{- 160 x ^{3} + 120 e ^{2 x} x ^{2} - 180 e ^{2 x} x - 240 x + 105 e ^{2 x} + 384 cos ( x )}{1920}

y = c_{1} + c_{2} e^{- 2 x} + c_{3} e^{2 x} + \frac{- 160 x ^{3} + 120 e ^{2 x} x ^{2} - 180 e ^{2 x} x - 240 x + 105 e ^{2 x} + 384 cos ( x )}{1920}

(d^{2} + 6 d + 10) y = 3 x e^{- 3 x} - 2 e^{3 x} cos (x)

y^{^{''}} + 2 y^{^{'}} - 8 y = 6 e^{- 3 x} - e^{- x}

y^{^{''}} + y = \frac{1}{cos ( t )}

y^{^{''}} - 6 y^{^{'}} + 9 y = 3 x^{2} + 4 e^{4 x}

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