(d^2y)/(dx^2)-(dy)/(dx)-45y=e^{5x}

Lösung

\frac{d ^{2} y}{d x ^{2}} - \frac{d y}{d x} - 45 y = e^{5 x}

y = c_{1} e^{\frac{( 1 + 181 ) x}{2}} + c_{2} e^{\frac{( 1 - 181 ) x}{2}} - \frac{1}{25} e^{5 x}

Schritte zur Lösung

\frac{d ^{2} y}{d x ^{2}} - \frac{d y}{d x} - 45 y = e^{5 x}

Solve linear ODE:

y = c_{1} e^{\frac{( 1 + 181 ) x}{2}} + c_{2} e^{\frac{( 1 - 181 ) x}{2}} - \frac{1}{25} e^{5 x}

y = c_{1} e^{\frac{( 1 + 181 ) x}{2}} + c_{2} e^{\frac{( 1 - 181 ) x}{2}} - \frac{1}{25} e^{5 x}

\frac{d ^{2} x}{d t ^{2}} + 36 x = 10 sin (4 t)

y^{^{''''}} - y = 1, y (0) = 0, y^{^{'}} (0) = 0, y^{^{''}} (0) = 0

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

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

4 y^{^{''}} - 4 y^{^{'}} + y = 72 e^{\frac{t}{2}}