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

Lösung

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

y = c_{1} + c_{2} e^{- x} + c_{3} e^{x} + 2 x e^{- x} - \frac{3 e ^{2} x ^{2}}{2}

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} + c_{2} e^{- x} + c_{3} e^{x} + 2 x e^{- x} - \frac{3 e ^{2} x ^{2}}{2}

y = c_{1} + c_{2} e^{- x} + c_{3} e^{x} + 2 x e^{- x} - \frac{3 e ^{2} x ^{2}}{2}

(d^{2} + 4) y = e^{3} x

(d - 1)^{2} \cdot y = sin (x) \cdot x^{2} \cdot e^{x}

(d^{3} + 1) \cdot y = cos (2 x - 1)

y^{^{''}} + y^{^{'}} + y = x^{2} + 3 x

(d^{2} + 9) y = sin^{3} (x)