y^{''}-3y^'+2y=sqrt(x+1)

Lösung

y^{^{''}} - 3 y^{^{'}} + 2 y = x + 1

y = c_{1} e^{2 x} + c_{2} e^{x} - \frac{2 2 x + 2}{4} + \frac{2 e ^{2} π}{8} e^{2 x} erf (2 x + 2) + e^{x} \cdot \int - \frac{x + 1}{e ^{x}} d x

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} e^{x} - \frac{2 2 x + 2}{4} + \frac{2 e ^{2} π}{8} e^{2 x} erf (2 x + 2) + e^{x} \cdot \int - \frac{x + 1}{e ^{x}} d x

y = c_{1} e^{2 x} + c_{2} e^{x} - \frac{2 2 x + 2}{4} + \frac{2 e ^{2} π}{8} e^{2 x} erf (2 x + 2) + e^{x} \cdot \int - \frac{x + 1}{e ^{x}} d x

y^{^{''}} - 4 y^{^{'}} + 4 y = t^{2} e^{2 t}

(d^{3} - 3 d) y = 9 x^{2}

y^{^{''}} + y^{^{'}} - 12 y = 4 e^{x} sin (2 x) + 4 e^{3 x} + 2

\frac{d ^{2} y}{d x ^{2}} + \frac{d y}{d x} + 2 y = 5 e^{3 x}

\frac{d ^{2} y}{d x ^{2}} + 2 \frac{d y}{d x} - 15 y = (x + 1) e^{x}