y^{''}-8y^'-4y-2=10x^2-2xe^2

Lösung

y^{^{''}} - 8 y^{^{'}} - 4 y - 2 = 10 x^{2} - 2 x e^{2}

y = c_{1} e^{2 (2 + 5) x} + c_{2} e^{2 (2 - 5) x} - \frac{5 x ^{2}}{2} + \frac{( 2 e ^{2} + 40 ) x}{4} - \frac{4 e ^{2} + 87}{4}

Schritte zur Lösung

y^{''} (x) - 8 y^{'} (x) - 4 y - 2 = 10 x^{2} - 2 x e^{2}

Solve linear ODE:

y = c_{1} e^{2 (2 + 5) x} + c_{2} e^{2 (2 - 5) x} - \frac{5 x ^{2}}{2} + \frac{( 2 e ^{2} + 40 ) x}{4} - \frac{4 e ^{2} + 87}{4}

y = c_{1} e^{2 (2 + 5) x} + c_{2} e^{2 (2 - 5) x} - \frac{5 x ^{2}}{2} + \frac{( 2 e ^{2} + 40 ) x}{4} - \frac{4 e ^{2} + 87}{4}

y^{^{''}} - y^{^{'}} - 6 y = 22 cos (3 x)

9 y^{^{''}} + 6 y^{^{'}} + y = 2, y (0) = 0, y^{^{'}} (0) = 0

y^{^{''}} - 4 y^{^{'}} + 4 y = t

y^{^{''''}} + 4 y^{^{''}} = sin (2 t) + t e^{3 t} + 4

y^{^{''}} - y^{^{'}} - 12 = 0