y^{''}-12y^'+36y=te^{6t}

Lösung

y^{^{''}} - 12 y^{^{'}} + 36 y = t e^{6 t}

y = c_{1} e^{6 t} + c_{2} t e^{6 t} + \frac{e ^{6 t} t ^{3}}{6}

Schritte zur Lösung

y^{''} (t) - 12 y^{'} (t) + 36 y = t e^{6 t}

Solve linear ODE:

y = c_{1} e^{6 t} + c_{2} t e^{6 t} + \frac{e ^{6 t} t ^{3}}{6}

y = c_{1} e^{6 t} + c_{2} t e^{6 t} + \frac{e ^{6 t} t ^{3}}{6}

\frac{d}{d x} (\frac{2 + sin ( x )}{2 x + cos ( x )})

5 t \frac{d y}{d t} - 5 y = t

\frac{\partial}{\partial y} (\frac{y}{x ^{2} + y ^{2}})

\frac{\partial}{\partial x} (x^{3} z + yz)

\frac{d}{d x} (\frac{1}{( 2 x + 1 ) ^{2}})