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

Lösung

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

y = c_{1} e^{x} + c_{2} x e^{x} + e^{x} ln (cosh (x))

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} e^{x} + c_{2} x e^{x} + e^{x} ln (cosh (x))

y = c_{1} e^{x} + c_{2} x e^{x} + e^{x} ln (cosh (x))

\frac{d ^{2} y}{d x ^{2}} - 4 \frac{d y}{d x} + 36 y = 4

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

y^{^{''}} + 6 y + 34 = 0, y (0) = 1, y^{^{'}} (0) = 7

y^{^{''}} + 25 y = 2 cos (5.1 t), y (0) = 1, y^{^{'}} (0) = 1

2 y^{^{'}} - 3 = - y + y^{^{''}} + 16 e^{3 x} + 3 e^{2 x} + 5