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Beliebt Rechnen >

16y^{''}-72y^'+81y=0,y(0)=8

Lösung

16 y^{^{''}} - 72 y^{^{'}} + 81 y = 0, y (0) = 8

Lösung

y = 8 e^{\frac{9 t}{4}} + c_{2} e^{\frac{9 t}{4}} t

Schritte zur Lösung

16 y^{''} (t) - 72 y^{'} (t) + 81 y = 0

Solve linear ODE:

y = 8 e^{\frac{9 t}{4}} + c_{2} e^{\frac{9 t}{4}} t

y = 8 e^{\frac{9 t}{4}} + c_{2} e^{\frac{9 t}{4}} t

Graph

Beliebte Beispiele

y^{'''}-2y^{''}-40y^'-64y=0

y^{^{'''}} - 2 y^{^{''}} - 40 y^{^{'}} - 64 y = 0

(d^2f)/(dx^2)+k^2f(x)=0

\frac{d ^{2} f}{d x ^{2}} + k^{2} f (x) = 0

2y^{''}+3y^'=0,y(0)=1,y^'(0)=1

2 y^{^{''}} + 3 y^{^{'}} = 0, y (0) = 1, y^{^{'}} (0) = 1

x^{''}+8x^'=0,x(0)=-3,x^'(0)=5

x^{^{''}} + 8 x^{^{'}} = 0, x (0) = - 3, x^{^{'}} (0) = 5

y^{''}-6y^{''}+8y=0

y^{^{''}} - 6 y^{^{''}} + 8 y = 0