(d^2y)/(dx^2)-5(dy)/(dx)+6y=x^3+x

Lösung

\frac{d ^{2} y}{d x ^{2}} - 5 \frac{d y}{d x} + 6 y = x^{3} + x

y = c_{1} e^{3 x} + c_{2} e^{2 x} + \frac{x ^{3}}{6} + \frac{5 x ^{2}}{12} + \frac{25 x}{36} + \frac{95}{216}

Schritte zur Lösung

\frac{d ^{2} y}{d x ^{2}} - 5 \frac{d y}{d x} + 6 y = x^{3} + x

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} e^{2 x} + \frac{x ^{3}}{6} + \frac{5 x ^{2}}{12} + \frac{25 x}{36} + \frac{95}{216}

y = c_{1} e^{3 x} + c_{2} e^{2 x} + \frac{x ^{3}}{6} + \frac{5 x ^{2}}{12} + \frac{25 x}{36} + \frac{95}{216}

y^{^{''}} + 10 y^{^{'}} + 16 = 0

y^{^{''}} + 153.06 y^{^{'}} + 12739.6 y = 191094.97

\frac{d ^{3} y}{d x ^{3}} + y = e^{- x} + 1

\frac{d ^{2} y}{d x ^{2}} + \frac{d y}{d x} - 20 y = e^{- 5 x}

y^{^{''}} - y^{^{'}} - 16 = 0