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Beliebt Rechnen >

(d^2y)/(dt^2)-12(dy)/(dt)+36y=7+4t

Lösung

\frac{d ^{2} y}{d t ^{2}} - 12 \frac{d y}{d t} + 36 y = 7 + 4 t

Lösung

y = c_{1} e^{6 t} + c_{2} t e^{6 t} + \frac{t}{9} + \frac{25}{108}

Schritte zur Lösung

\frac{d ^{2} y}{d t ^{2}} - 12 \frac{d y}{d t} + 36 y = 7 + 4 t

Solve linear ODE:

y = c_{1} e^{6 t} + c_{2} t e^{6 t} + \frac{t}{9} + \frac{25}{108}

y = c_{1} e^{6 t} + c_{2} t e^{6 t} + \frac{t}{9} + \frac{25}{108}

Graph

Beliebte Beispiele

linear y^{''}+y^'+2y=sin(x)

l in e a r y^{^{''}} + y^{^{'}} + 2 y = sin (x)

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

y^{^{''}} - 2 y^{^{'}} + 2 y = e^{(2 x)} \cdot sin (x)

y^{''}-15y^'+54y=e^{ax}

y^{^{''}} - 15 y^{^{'}} + 54 y = e^{a x}

y^{'''}+9y^{''}+y^'+9y=16e^x-9

y^{^{'''}} + 9 y^{^{''}} + y^{^{'}} + 9 y = 16 e^{x} - 9

y^{''}+8y^'+32y=2e^{2x}

y^{^{''}} + 8 y^{^{'}} + 32 y = 2 e^{2 x}