y^{''}-6y^'+5y=3^x

Lösung

y^{^{''}} - 6 y^{^{'}} + 5 y = 3^{x}

y = c_{1} e^{5 x} + c_{2} e^{x} + \frac{( ln ( 3 ) - 1 ) \cdot 3 ^{\frac{( - 5 + l n ( 3 ) ) x}{l n ( 3 )}} e ^{5 x} - ( ln ( 3 ) - 5 ) \cdot 3 ^{x}}{4 ln ^{2} ( 3 ) - 24 ln ( 3 ) + 20}

Schritte zur Lösung

y^{''} (x) - 6 y^{'} (x) + 5 y = 3^{x}

Solve linear ODE:

y = c_{1} e^{5 x} + c_{2} e^{x} + \frac{( ln ( 3 ) - 1 ) \cdot 3 ^{\frac{( - 5 + l n ( 3 ) ) x}{l n ( 3 )}} e ^{5 x} - ( ln ( 3 ) - 5 ) \cdot 3 ^{x}}{4 ln ^{2} ( 3 ) - 24 ln ( 3 ) + 20}

y = c_{1} e^{5 x} + c_{2} e^{x} + \frac{( ln ( 3 ) - 1 ) \cdot 3 ^{\frac{( - 5 + l n ( 3 ) ) x}{l n ( 3 )}} e ^{5 x} - ( ln ( 3 ) - 5 ) \cdot 3 ^{x}}{4 ln ^{2} ( 3 ) - 24 ln ( 3 ) + 20}

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

y^{^{''}} + 4 y^{^{'}} = sin^{3} (x)

(d - 1)^{2} (d^{2} + 1) y = 3 x^{2} - 5 x + 2

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

(d^{2} - 13 d + 12) y = 2008