y^{''}-2y^'-3y=5e^4x,y(0)=1,y^'(0)=0

Lösung

y^{^{''}} - 2 y^{^{'}} - 3 y = 5 e^{4} x, y (0) = 1, y^{^{'}} (0) = 0

y = (1 + \frac{5 e ^{4} - 3}{4} - \frac{10 e ^{4}}{9}) e^{3 x} - \frac{5 e ^{4} - 3}{4} e^{- x} - \frac{5 e ^{4} x}{3} + \frac{10 e ^{4}}{9}

Schritte zur Lösung

y^{''} (x) - 2 y^{'} (x) - 3 y = 5 e^{4} x

Solve linear ODE:

y = (1 + \frac{5 e ^{4} - 3}{4} - \frac{10 e ^{4}}{9}) e^{3 x} - \frac{5 e ^{4} - 3}{4} e^{- x} - \frac{5 e ^{4} x}{3} + \frac{10 e ^{4}}{9}

y = (1 + \frac{5 e ^{4} - 3}{4} - \frac{10 e ^{4}}{9}) e^{3 x} - \frac{5 e ^{4} - 3}{4} e^{- x} - \frac{5 e ^{4} x}{3} + \frac{10 e ^{4}}{9}

9 y^{^{''}} + 4 y = 3 x + 12 e^{- x}

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

x^{^{''}} + 6 x^{^{'}} + 23 x = 12 cos (4 t)

(d^{2} + 9) y = 30 sin^{3} (x)

y^{^{''''}} - y = 11 t + cos (t)