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Beliebt Rechnen >

y^{'''}+4y^{''}-5y=xe^x+14x

Lösung

y^{^{'''}} + 4 y^{^{''}} - 5 y = x e^{x} + 14 x

Lösung

y = c_{1} e^{x} + c_{2} e^{\frac{( - 5 + 5 ) x}{2}} + c_{3} e^{\frac{( - 5 - 5 ) x}{2}} + \frac{e ^{x} x ^{2}}{22} - \frac{7 e ^{x} x}{121} - \frac{14 x}{5}

Schritte zur Lösung

y^{'''} (x) + 4 y^{''} (x) - 5 y = x e^{x} + 14 x

Solve linear ODE:

y = c_{1} e^{x} + c_{2} e^{\frac{( - 5 + 5 ) x}{2}} + c_{3} e^{\frac{( - 5 - 5 ) x}{2}} + \frac{e ^{x} x ^{2}}{22} - \frac{7 e ^{x} x}{121} - \frac{14 x}{5}

y = c_{1} e^{x} + c_{2} e^{\frac{( - 5 + 5 ) x}{2}} + c_{3} e^{\frac{( - 5 - 5 ) x}{2}} + \frac{e ^{x} x ^{2}}{22} - \frac{7 e ^{x} x}{121} - \frac{14 x}{5}

Graph

Beliebte Beispiele

y^{''}-2y^'+y=-5e^x+8x^2

y^{^{''}} - 2 y^{^{'}} + y = - 5 e^{x} + 8 x^{2}

y^{^{''}} + 9 y = 4 x

(D^4-4D^2)y=5x^2-e^{2x}

(D^{4} - 4 D^{2}) y = 5 x^{2} - e^{2 x}

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

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

y^{''}+25y=50sin(5t)

y^{^{''}} + 25 y = 50 sin (5 t)